Sorry that it took me so long to reply, viparagon...I've been too busy to give a well-thought-out reply lately.
Anyways, I'll do what summarizing that I can. If you, Mmac, or anyone else has any disagreement with my summarization, please do post; I don't want to suggest false information about the matchup. On that note, let's get started, shall we?
~As with any other matchup, proper spacing is key; however, be aware that his Dragonic Reverses and Dragonic Trots can really screw up your spacing if you aren't aware of them and/or don't see them coming. If you aren't aware of what these are (seeing as Yoshi isn't exactly the most commonly-played character), then go down to the 16th and 19th AT's in this Yoshi guide on Smashboards for an explanation and a video link of each:
*Yoshi Guide Link*
-Yoshi's grab game is very dangerous. He can chain grab you with grab releases and go for the fair spike when you get off the ledge. This spike is powerful and can kill you around 50% on most stages. He can also Grab Release-->Usmash for a star KO when you are around 110% on most stages. Yoshi can also choose to use a much wider variety of moves with which to follow up a grab release; in essence, it is VERY important that you avoid getting grabbed as much as possible (especially at high percents). The one weakness of this throw is that if it whiffs (from a spotdodge, etc.), the grapple properties of it scream of punishment from you with a move of your choice (except fsmash, of course).
-Although the CG is very dangerous, this doesn't mean that shielding is still not a smart option (at the right times). His smashes, for example, are quite punishable when shielded.
-Yoshi's air game is a lot better than one might give him credit for; his bair and uair come out pretty quickly (the uair being a reasonably good kill move), and his nair comes out very quickly. In addition, his quick, long-reaching bair (at certain angles) and possibly his dair (I'm not sure about the dair) can go through your tornado, as well as his tongue moves (his neutral B and his grab). Luckily, your aerial game has range and priority on his aerial game. Use this to your advantage, and space accordingly.
-Bairs are a dangerous, multi-purposed facet of Yoshi's game, but since they have little knockback, you can shieldgrab these, and should do so whenever you can. A smart Yoshi will use this as a hit-and-run tactic to pressure your shield, though; if this happens, it might be time to whip out an MT (or a tilt if he lands close enough to you). When you are at higher percentages (about 80%+), Yoshi might go past you with a bair and try to pivot grab you into a Usmash. Be wary of this option, and spotdodge the pivot grab when it comes and punish it...or you might be able to pull off a dsmash as Yoshi lands if you're quick enough.
-Dairs can be quite annoying shield-eaters; however, as mentioned earlier, you have better range with your attacks than his dairs do. If you are also in the air when he dairs, you can safely space a uair to counter his dair.
-Yoshi can be very hard to gimp because his second jump has a solid number of super armor frames during the start of the jump. Don't forget that he can airdodge or attack in the middle of that uber-long jump, too. If you do manage to eliminate Yoshi's second jump, though, his poor Up-B recovery makes him a very easy target for gimping; however, this is much easier said than done.
-Yoshi has some VERY nasty counterpicks on you, such as Castle Siege, Corneria, Green Hil Zone, and Distant Planet. Yoshi likes his stages because they either have walk-offs (Ex.: C. Siege (2nd stage), Green Hill Zone), walls where he can do infinite grab release combos on you (Ex.: Corneria), mostly-flat stage layouts (Ex.: C. Siege (3rd stage), Final Destination), or a combination of these elements. Luckily, you have some counterpicking factors on your side, as well; stages with platforms that are low to the ground (Ex.: Battlefield, Lylat Cruise) are great counterpicks because the platforms can catch you from a grab release, thereby destroying a good number of Yoshi's CG attempts. Also, in general, you fare better on stages that have lots of small platforms than Yoshi does, since your sword's disjointed hitbox is a big asset against Yoshi's aerials (don't forget that smaller platforms mean less chaingrabbing that Yoshi can do on them). Rainbow Cruise can be an excellent counterpick against Yoshi in this regard, but some of the walkoffs on the top of the rotation of the stage can be very deadly CG spots for Yoshi, so it's a double-edged sword.
-Don't underestimate Yoshi's eggs simply because they are an awkward projectile. The eggs have slight splash damage (due to the egg shards), and they actually have priority over every single one of your B moves -- even the Shuttle Loop. Your aerials can't cancel out the eggs, either. This leaves not too many options besides airdodging and fast falling in the air, which makes Yoshi's eggs a great anti-air tool.
That pretty much covers the bases. If Mmac or someone else could touch on the pivot grabbing topic, that would be awesome, because I don't know a whole lot about it.
I'm just throwing out my point of view for the interpretation of the masses, whether it be right or wrong. I just wanted to say that so that I don't offend anyone.
. Maybe I should do something like Xyro did.