This is definitely something that needs to be approached in steps, like Trip was getting at, so I'll try and break it up as best as I can. I'm gonna try and really go into some depth here, because this is something I'd like to improve at too and I don't think I've given it enough thought before now.
1. Learn (AKA commit to muscle memory) the timing for letting go of the edge. This is critical! There's a good chance you're aware of this already, but for anyone who's not, it's important to understand how a ledgegrab works. First off, a green ring appears around your hand when you grab the edge, which corresponds to the beginning of your invincibility. Sheik then enters a short animation during which she transitions into her "hanging" position. As soon as that animation is complete and she is hanging, you can let go. It's hard to see at normal speed, but if you slow it down in practice mode you'll see what I mean. Anyway, to practice, I'd recommend starting at 2/3 speed (I personally NEVER go slower than that) and either planking or shino stalling repeatedly until you start to get it, then switch to normal speed.
2. Develop long wavedashes - I would actually practice the WD on stage before applying it to this technique. The reason I say that is because ideally you're gonna want a nice long, crispy wavedash back on stage, so you want to make sure you're not practicing a crappy short WD that will get you punished. A long WD has the advantage of (1) getting you closer to center stage, (2) making you harder to hit/react to, and (3) putting you in your opponent's face faster. To get a feel for it, practice running across the stage and then tilting just slightly below the horizantal to get nice juicy WD's. Like Sharpman said, you'll ftilt if you keep the stick held in the direction of your WD and press A, so add that to the end of each WD. You can't attack right away after initiating a WD, so it's important to have a good feel for how long you have to wait (the natural tendency when you're doing a ledgedash-ftilt is going to be to rush the ftilt).
3. Refine the wavedash - One mechanical issue of ledgedashing is that your control stick is not going to be facing the stage when you first let go of the ledge; instead it will be directed either away from the stage or down, depending on how you decided to let go. Personally, I recommend NOT pushing down to let go because that puts you into a fastfall, which makes it a lot easier to mess up the timing on the ledgedash and kill yourself. Pushing away however means you have to move the control stick farther to execute the WD, so this is the next thing I would practice. To do so, practice running forward and then WD'ing back. Again, you want the WD to be as long as possible, which is why I recommended getting that down first. Once you've got that down, just add the ftilt back in to simulate the full technique.
4. Putting it together - Finally, you're almost ready to execute the whole thing. The last thing to work on is learning the timing to start the air-dodge after the double-jump. This is kinda tricky - as far as I can tell, there's two reasons why people SD doing this: 1. They air-dodge before they get the control stick aimed toward the stage and 2. they are too slow and drift too far away from the stage when they let go of the ledge, and their air-dodge misses the stage as a result. I've experimented with it, and it seems to me that the trick is to jam the control stick towards the stage as fast as possible - I don't think it's possible to be "too fast" as long as your control stick is correctly placed when you air-dodge, but I could definitely be wrong. Getting a feeling for this timing is really the key to the whole thing, though, so it's super important. Once you've got it, you're good to go with the whole technique, and it's all about just practicing and refining it from there.
Edit: I realized some of my assumptions in 4. were wrong when I tested out my own advice, so I tried to correct it as best as I could =P