I am not sure how to refer to them, but on my back I have two "plates" that stick out. If you take a look at me from the side, my back tends to stick out. I guess I don't really have a strong build of muscle there, but how exactly do I get my back to not stick out as much? Should I do more push ups?

Is it your shoulder blades? Possibly this is the case because you have rounded shoulders? But I dont think anyone can tell without a really good description or pictures.

Sounds as though your refering to your scapula (shoulder blades)..

The mucles thats duty is to ensure the scapula is bounded onto the thorax are the serratus anterior muscle and the rhomboids. Try working these muscles, which will include retraction and upward rotation exercises im sure some of our gym enthusiasts can give you some particular exercises to work with

And make sure your posture is up to scratch.

I sent you a pm

Absolutely not! In fact, that's a bad thing to do. It's a bit hard to grasp what you're talking about without a pic but from your description i'm guessing that your shoulders are probably rolled forward, which is making your scaps stick out. It means that you have a muscle inbalance between your front and back. Stretch your chest out and do some lower trap exercises. This will help *pull* your shoulders back. and just do some more back work overall and less chest and anterior delt work. But like i said, you'd be best to post up a pic so we can see exactly what you're talking about.

while it can sound like a posture problem, we need pics to clarify, all skinny people have their scapulae sticking out.

Pushups can help, if you do pushup plus, which will work the serratus anterior. If his shoulderblades are rotated downward, he probobly doesnt need rhomb work, but lower and upper trap and serratus anterior work.

We need to determine if his scapulae is rotated downward (weak serratus, upper and lower trap. rhomb and lats probobly tight), if his shoulderblades are pulled forward (tight chest, weak back in general), or both at the same time.

Anyways, it could just be that he has small back muscles, id do some rows, face pulls, pullups, deadlift etc to build it up.
anyways, id recommend you to post some pictures of your back from the side and from the back so we can determine what your problem is.