Ivysaur
Jab - Ivysaur swings two vines directly forward, one after the other. Every hit has pretty good range. The first hit has decent speed, and can be used to stuff slower moves. The second hit is generally utterly terrible, as it is easy to shield or avoid even if the first jab hits, which will get you punished easily. After the first two swings, it goes into a rapid-fire swinging that cannot be shielded in-between hits. This rapid-fire portion also has slightly more range, which makes it very safe from most approaches once the rapid-fire portion starts. It makes for a decent option against opponents near or on the edge, but this is usually a move that you want to avoid.
Dash Attack - Ivysaur slides on the ground. This move is powerful for a dash attack; it is fast, and it KO's reliably at about 150%, but it is unsafe when shielded and doesn't have much range. Keep it in mind when the opponent is left open, or when they are at a high percentage, but this is not nearly as spammable as Squirtle's.
Forward-Tilt - Ivysaur leans forward and spins some leaves around. This attack is quite good in many ways; it starts quickly, deals respectable damage, has great range, hits multiple times, and is difficult to punish with good spacing. The fact that it hits multiple times makes it a wonderful move for poking shields; if the opponent's shield is anything but full, they're getting shield-poked, which makes it a wonderful follow-up to a late Back-Air. The fact that Ivysaur leans forward before using the attack helps make this move safe even when shielded; when the move is finished, Ivysaur moves back to a neutral stance quickly, which prevents shield-grabs against anyone that isn't Dedede or Charizard...and you should be able to land an easy B-Air on those shields in order to shield-poke anyway. One thing that you must take note of, however, is that it doesn't hit "on top of" Ivysaur. If you use this move while they're extremely close, they'll only take a couple hits, and you will be easy to punish...otherwise, this move is fairly spammable; always keep it in mind when you space or approach.
Up-Tilt - Ivysaur pushes against the ground with vines, propelling herself upwards. I have mixed feelings about this move. It has nice range above your standing position, but Ivysaur is the hitbox, making it easy to hit Ivysaur out of this move. It doesn't deal much damage or knockback, but it is relatively fast and can catch people off-guard. Also, when you do this move, since Ivysaur is on her vines, the opponent cannot hit Ivysaur as if she was on the ground. Perhaps this could be used as a potential dodge against certain moves, but more testing should be done. This is pretty good for hitting opponents on platforms, because it's fast, but Ivysaur has more damaging options. Use the range well, but don't rely on this to hit from below.
Down-Tilt - Ivysaur uses her whips to strike at the foe. This move is excellent; decent damage, gimp-worthy knockback, very good range, great speed, and it hits twice. The speed, combined with the fact that it hits twice, helps with shield-poking and keeps you from getting punished. This is among Ivysaur's best options when edgeguarding, and a wonderful move for spacing. When there's too little space to justify doing a RAR'd Back-Air, this is going to be your move of choice. Don't be afraid to use it often. Also, it should be noted that this move isn't nearly as fun for us on the edges of Yoshi's Island, because ledge makes it so that you must be quite close to edgeguard correctly, and this move is all about safe outranging. Keep that in mind.
Forward-Smash - Ivysaur leans back and springs her body forward. This move has nice knockback; it KOs consistently in the triple digits. The range on it is pretty good, as well; Ivysaur suddenly moves quite forward during the attacking portion. Still, as a Forward-Smash, it's not very quick to come out, so you're not going to land this by throwing it out by itself. One thing that I find myself doing often is doing a Forward-Smash out of an initial dash in the opposite direction. Basically, if you are within the timing where you could do a dashdance, you can use a Forward-Smash in either direction, which is easily done by using the C-Stick. On aggressive players, you can initial dash backwards and do it, which functions sort of like a mini-dodge. It's nice to catch people off-guard, so keep that in mind.
Up-Smash - Ivysaur strains for a time, and then fires an explosion of pollen (I like to think of it as Stun Spore, actually) into the air from her flower. This move is quite slow to come out, but is arguably the best "kill at ridiculously low percentages" Smash attack there is, since the animation isn't as long or elaborate as Dedede/Ike F-Smash, while it has almost as much knockback. One thing to note is that it actually doesn't do that much damage; I believe it deals 17% uncharged, but when it kills reliably at 75%, it doesn't matter that much. It doesn't have a much cooldown time, either, although you can still be punished if it misses completely. This is a move that you should learn to hit with; the sheer power is too high to ignore. The easiest way to land it is to predict an air-dodge to the ground. When you get good at timing this, it's the most satisfying attack to use, and it's a force to be reckoned with. The hitbox is also fairly high up, so you can hit opponents on some platforms, like on Battlefield. Think about that.
Down-Smash - Ivysaur does a sweeping motion with vines on both sides. Terrible knockback, terrible damage (D-Tilt does more!), annoying cooldown, no sweetspot, hits once, and only hits very close to the ground. It is, in essence, a very bad D-Tilt. The only thing it has going for it is that it hits on both sides, but if you're questioning which side the opponent is going, you may as well attempt a Bullet Seed. Stay away from this move at all costs. There is currently no good use for it, to the best of my knowledge.
Neutral-Air - Ivysaur spins around diagonally-downward. This move is Ivysaur's bread-and-butter in terms of combo ability. It hits multiple times, deals good damage (about 14% if all parts of it hit), has very little landing lag, and doesn't send the opponent far away on the last hit. As a multi-hit move, you should keep this in mind as a shield-poking option; that's how you safely start the various combos that stem from this move. The first few hits actually don't send the opponent anywhere to begin with. In that, it's quite easy to do a N-Air into the ground and immediately do a N-Air again. Depending on the percentage, a single full-hopped N-Air can lead into another N-Air, F-Air, B-Air, or U-Air. Platforms also increase this move's comboability. Just experiment and you'll find that you can do so much in that way.
One cool thing about Ivysaur's Neutral-Air is that the back/bottom portion of Ivysaur's Neutral-Air is a genuine spike; just move away from the opponent mid-attack and you'll land it. It's not particularly powerful, but it's usually enough to get the job done, or at least let you attempt to finish the job afterwards. It's hard to see coming, and is a great skill to learn.
Forward-Air - Ivysaur uses her vines as a whip in a forward arc from top to bottom. This move has deceptive range and speed, so using this to defend yourself while recovering is good. It has pretty good KO power, and will reliably kill at about 125%. If you short-hop F-Air, it will have no landing lag as long as you do the F-Air immediately after the jump. Otherwise, it has a fair amount of landing lag, so be careful about using this while close.
Up-Air - Ivysaur does a quick pollen explosion from her flower. This move is quite powerful for an aerial; it reliably kills at about 100%, even on heavier characters. The range is deceptive; some of the hitbox is actually Ivysaur's body, so it's not unheard of to hit an opponent who is below you! It pushes an opponent back if they shield it, so doing it before you land is pretty safe, as long as they don't powershield. If you are in the air and chasing a recovering opponent, you can bait an air-dodge and land this move afterwards. This move is something that an opponent will fear in an air battle. Using this move in mid-air
Down-Air - Ivysaur turns her flower towards the ground and fires a pollen explosion downwards. This move has decent knockback, and decent power. When you use it, you lose aerial mobility until you flip right-side up, so keep this in mind. The main thing to keep in mind is that this move is a Meteor Smash, but the sweetspot is the flower, not the explosion that comes out. If you land the sourspot, it sends the opponent horizontally, which isn't necessarily a bad thing, but isn't as good as a Meteor Smash. This move also has a lot of landing lag, so be very careful not to do this move too late while above the stage. One nice but fairly risky tactic to keep in mind is that a short-hopped D-Air will go through platforms as long as the attack has enough time to come out. You can use this to hit opponents underneath you while you are on a platform...and if you are on a stage like Halberd or Delfino and the opponent decides to attack you from below the stage, give them a surprising hit straight down. They won't know what hit 'em.
Back-Air - Ivysaur swings two vines in a 270-degree arc from the top-and-behind to the bottom-and-behind. This move is arguably the best spacing move in the entire game; it has absolutely obscene range, great speed, hits twice, has virtually no landing lag, and allows you to do another move almost immediately afterwards. This move will make it a nightmare for most characters to get in on Ivysaur. It does very little damage, but when you're not getting hit, it's always a winning decision. This move also has combo potential; if you land immediately after a B-Air, you can B-Air again from another jump. If the opponent takes the move (whether it's shielded or an actual hit), you can do a F-Tilt immediately afterwards, and it will hit the opponent. B-Air -> F-Tilt is going to be your main option for shield-harassment.
Because of Ivysaur's terrible horizontal aerial mobility, the opponent's shield must be down in order to reliably and safely combo. You can accomplish this by using short-hop mindgames. A short-hopped B-Air should not be getting punished by itself, but that doesn't mean that he can't shield it and attempt to get in. To stop that, you should mix up your timings. Empty short-hops, late B-Airs, full-hop B-Airs, double-jump double B-Airs...they're going to end up shielding a lot, so it helps you set the pace and trick him into a faulty defense.
Neutral-B - Ivysaur hits the opponent up with an invisible force, and fires seeds up out of her flower. This move is a punisher's dream: comes out on Frame 4 (the same as many jabs), covers both sides of Ivysaur on the initial hit, and deals on average about 30%. Use this against roll spammers, spot-dodges, late air-dodges to the ground, out of a shield after they attack...basically, any time they make a mistake on the ground, you should be able to have an opening to land this move. Because the only thing the opponent can do when they are caught in this move is hold a direction and wait it out, this move can get annoying quite fast, as no one likes losing control of their character for any amount of time. Also, because it comes out so quickly, you can use this move in the middle of some multi-hit moves, such as jab combos. This move gets people flustered, so depending on the player and the situation, landing this move repeatedly can be better than a grab or Smash attack. If they can't think, they can't play.
While this sounds absolutely wonderful (and it is), it's highly punishable when you miss. If the opponent sees it coming, they can charge the Smash of their choice and leave quite a mark. You'll learn the right times to land this simply by experimenting in matches, so get to throwing it out and find out when it's fine to use it.
Forward-B - Ivysaur throws a leaf forward as a projectile. This is rather good; it eats many projectiles and keeps going, and it's usually difficult to cancel with a normal move, so it's rather spammable. If you short-hop before throwing it, you can still move in mid-air while using the move, so short-hopping this move is usually the best way to do it. It deals minor damage, but every bit counts, and it's difficult to stop, so it adds up fairly quickly. Depending on the distance and percentage, you can grab an opponent out of the hitstun of this move. It's also a bit of a reflex for the opponent to attempt to side-dodge the leaf or your follow-up move, so attempting a pivot grab or short-hopped N-Air/Bullet Seed as a follow-up is satisfactory. Just be safe with it, and it will serve you well as a troublesome projectile.
Up-B - Ivysaur stretches a vine at an upward angle. This move is a tether recovery, so if the opponent is on the ledge, you will fall to your doom. It has a larger range than it would suggest when used on-stage, so experiment and know the exact distance and angles by heart. Ivysaur's bad aerial mobility makes her fairly easy to edgeguard compared to most characters, so learn how to properly use F-Airs, B-Airs, and Razor Leaf to clear the edge. As for using it in an offensive manner, the move is straightforward, and normally has little knockback. Decent damage, though...however, the sweetspot, which is the tip of the move, has amazing knockback, and will kill at as early as 70%. You can quickly grab and re-grab the ledge with a tether recovery to quickly regain ledge invincibility, and depending on your angle, you can hold the edge while preventing the opponent from recovering. Once again, experimenting is the best way to learn for this.
Down-B - Switches to Charizard. Unlike Squirtle and Charizard, Ivysaur does not have a move that allows you to safely switch, so you'll simply have to use your better judgement.
Standing grab - Ivysaur reaches out with two vines in order to grab the opponent. Somewhat slow for a standing grab, but great range. Careful that you don't leave yourself open.
Running grab - A lunging version of the standing grab. Better range, but leaves you more open if you miss. Use your best judgement in order to tell which is better for the current situation.
Grab-pummel - Ivysaur constricts the opponent. Decent damage (about 2.5% each hit), but a bit slow. Try to get as many as possible before throwing, because each hit really adds up.
Forward-Throw - Ivysaur pushes the opponent forward with vines. Good damage, and decent knockback, but not a killing throw. Use this throw when it will get the opponent off the edge.
Up-Throw - Ivysaur pushes the opponent up with vines. This throw has the most knockback, and will reliably kill after 160%. Ivysaur has a lot of potential to deal damage, so don't forget this.
Down-Throw - Ivysaur slams the opponent against the ground with vines. It pops the opponent up and forward, and doesn't have a lot of knockback, so it can be a decent option for following up. Still, nothing spectacular.
Back-Throw - Ivysaur slings the opponent backwards. This throw is quite quick, and has pretty good knockback. Use this throw when it will get the opponent off the stage.