I have a couple of things that may be useful.
Start your way up a CPU from level (whatever you're comfortable with) to level 9. This is ONLY to get used to your character's moves. How long smashes take, how spaced you should be to start up an attack safely, getting used to short-hopped attacks, how to set up and kill, etc...
Once you're comfortable with your character, run down to level 3 or so. 3 is a good number, but you can go lower if you want. Now, choose something you feel is a weakness. If you have someone to play against, play a relatively serious match, and just watch the replays. Analyse yourself. What moves do you never do? Why do you keep dying? What moves do you keep trying but don't connect with?
Practice these weaknesses against a CPU. If dodging and blocking is a problem, then play the entire match just trying to not to get hit. Don't even attack. Just don't get hit. Slowly incorporate some counters only if you know you won't get hit. Practice defense, offense, locks, spikes, setups, dodging, KOs, whatever it is you need practice with.
Once you've got the basics, practice learning tricks. Brawl is a glitch factory. Find the characters tricks and ATs in their forum and practice them.
Along the way, whenever you have the chance, play against a real person. Nothing beats the real deal. You may notice that moves that always work on CPUs (like spammed projectiles) won't work on humans. Adjust accordingly.
Next, watch some vids. TWatch whatever videos you want, by whoever you want, but just always be aware of what moves they could have/should have done, and when. You'll notice a good player is all about proper timing and spacing. You need to wait for the right opportunity for many moves, so find a way to make them happen, and strike when they do.
A good player, no matter which character, is always in control. There is an inate human tendancy to want to do a move, and keep trying to get that move to connect. If you're one of those people that do that, then STOP. There is nothing worse than predictability. Get used to other characters. CPUs semi-work here, but again, nothing beats the real deal. Watch them and consider what possibilities they have at every turn. Being one step ahead will keep you safe and able to punish in advance.
Know the character inside and out. What KO moves work at what %ages, how to use them properly, how to sweetspot, all that stuff. Not every character KOs the same way - i.e. Zelda tends to KO through spikes our U-smashes/U-airs, while Sheik's weaker attacks mean she has to KO to the sides of the stage. Basically, just get used to how your character works as an individual.
Next up, recoveries. Just as much as you need to KO, you need to know how to recover if you're playing someone good. Remember those tricks/glitches? Find out if they work as recoveries. If not, learn how to DI properly.