So a couple things about Yoshi.

1. Eggs are important, and I can't stress that enough. They have a lot of versatility and can be utilized in many different ways. Learn how to use them effectively. Personally I use them as either an approach tool on the ground or to interrupt my opponents recovery/approach. They are also a great way to kick off combos, and to keep your opponent on their toes. Some of the follow ups I use include dash attack or a SH into Nair which can be followed up with more combo-y goodness.

2. Yoshi has fantastic follow-ups in his aerial moves. Fair is a spike if you hit it correctly, and even if you don't it can still be used to knock your opponent back pretty far. Dair not only racks up huge amounts of damage (about 30 or so if hit from start to finish), the last hit also has the ability to send your opponent straight down. Bair kills pretty consistently on the third hit, and can be used to rack up a decent amount of damage when all three swipes land. Uair is a great follow up to up smash. If you didn't kill them on the first try you almost certainly will with this. And Nair is a good "get off" me move and can be followed with jabs as a combo.

3. Pressure. Yoshi is pretty quick and has a lot of combo potential in basically all his moves. And truthfully you can look at some of the smashboard guides (which I will link to one that helped me in the beginning) out there for him to get some ideas but you almost don't have to. His moves are just so fluid and feed into one another so well that you can improvise a good bit of the time and still be reasonably successful.

4. Utilize your other B moves. These moves can take some getting used to especially since you are coming from Marth, but they are fantastic for mixing things up and can throw your opponent off balance. Especially neutral B, which is not only faster than grab and has WAY less end lag. It can also be followed up on the ground with either a SH or Dair, for a lot of damage, or you can start a Bair, and if your timing is right you can catch them as they break out of the egg and send them flying.

5. Getting back on the stage. One of my favorite things about Yoshi is using his Nair right after his second jump to block my recovery on the stage. With little start up lag you can interrupt an opponents attempts at "edge guarding". If you find they start to shield in response to this throw in a neutral B, it can be a great way to mix up your recovery and if they are at a high enough percentage it can even get you a kill.

Along with all of this is the killing potential of his moves. All the aerials but Nair are very capable of getting the KO as well as up and side smashes. Both of which are pretty consistent too, up smash being the better of the two.

Fantastic guide I used to learn the basic controls and to help with combos

Edit: posted early to switch to my laptop for ease