well, here's a few different ways that I can think of, and remember that it's 3:30 in the morning, so I may forget something =P
all of the below is assuming that you start hanging on the edge
1. standard edge recovery stuff: your basic attacking, jumping, and rolling from the edge. I try not to use these very often as their lag afterward can be punishable
2. double jumping: quickly dropping off the ledge and double jumping as soon as you leave it. In most cases this is a pretty safe bet, as you'll have your double jump protection to get you past most attacks that will come your way, though if your damage is high or your opponent is spike happy, you could end up losing your jump and falling to your doom. You can DJC into attacks as you come up onto the stage as well, just make sure that if your opponent is attacking, that you wait til after he attacks to make your attack, otherwise you're off the stage again, this time without a jump. Alternatively, you can try to space your double jump so that you don't pass right by the edge of the stage and still fly over your opponent, though this is difficult to do.
3. Wave Landing: Yoshi is particularly easy to waveland with out of his double jump, so this is a pretty useful option. Like #2, you can avoid getting knocked off by any immediate attacks with yoshi's double jump abilities (only for the first few frames, as you'll want to waveland quickly,) and you can do a variety of things out of a wavelanding. I like to mix it with a sidestep so that my opponent can't knock me back off the edge, although his sidestep is rather crap, so don't overly rely on this. like #2, you've gotta watch out for spikers and attacks in general at high damages, and once you waveland, remember that you no longer have that DJ protection. This also takes a slight amount of practice, cause if you do it too early, you'll simply airdodge into the side of the stage and fall to your doom. Obviously if you do it too late it's just an airdodge.
4. Double jump into airdodge: a bit tricky to get the positioning down with, but it's pretty safe unless your opponent's expecting it. Basically you want to drop off the ledge, and double jump so that you keep your distance from the edge until you want to airdodge. Hopefully you can either get behind your opponent or threw his timing off and caused him to attack early. Of course, if he waited, then he'll just send you back off with a tilt or (maybe charged) smash, so this also has its risks.
5. edge cancelled eggs (ECE): see the pinned yoshi thread for a better explanation of this one, but basically using option #2 but as soon as you're at/slightly above edge level, you use your egg toss. You'll grab the ledge after tossing the egg. If you're really good at it (see just about any video of fumi to know what good is,) you can keep this up for a while, and send your opponent scrambling for cover. However, if you're not too good at this, you can either kill yourself by using the egg toss too early or get killed by your opponent by jumping too high and putting yourself in danger of being hit. It takes a lot of practice, but it's a good option once you get it down (just don't spam it, the risks for #2 also apply here.)
6. Egg Roll: hitting back on the control stick to get off the edge quickly followed by a DJ + egg roll in the direction of the stage. The slight elevation gained by the attack will get you back on the stage. This attack in general isn't very good, so I wouldn't rely on it much unless you wanna have fun and you don't have someone waiting for you by the ledge to make a move.
There, that's all I can think of. If I didn't make something clear or said something I shouldn't have, I blame my sleepyness =P
OK, I've edited this for the last time to add more stuff, I'm going to bed >.< =P
I'm going to paste the suggestions that people post in the thread here so it's all in one place.
Rob_Gambino said:
When you go over them with a double jump waveland on a platform, so you get your jump back. Don't forget the basic ones like pressing L or attack too. Throw an edge cancelled egg and then waveland on to the stage works well if they're not in your face.
rmusgrave said:
My favourite move is the mid-air dodge on an angle so that you hover only just above the edge (goal is to be 1 frame of falling from landing). This way, you have invincibility followed by lag that is only as long as your wavedash, and the mid-air dodge time gives you time to DI properly.
This can dodge the entire Sheik downsmash animation!!
eltrotraw said:
If at high percents, ignore using any basic edge-getup techniques except for the plain standing up one.
In fact, I think the standing up one is the safest for Yoshi at any percent(though I think the same way for any character) since you can do whatever once you're back up, and it's the fastest.