A variety of pushups will strengthen your arms and shoulders. Do a search for bodyweight exercises and you'll find a bunch. You can get really strong doing a ton of hindu pushups (technique first, volume second), but mix it up to keep your body guessing.
For abs same thing, there are a bunch of core exercises (don't just do crunches) you can do without equipment. I just finished making a medicine ball that's great for your core. Buy a cheap basketball - start with a small one (got one for $5), and a bag of sand ($6). Cut |_ shape into ball, pour in sand, seal with glue and duct tape. A full-size basketball ended up being about 25lbs, which is a lot to start with, so a smaller ball will be better. Excellent "equipment" for almost no money.
Just some ideas. Also start doing some research on proper diet. To change your body you need to change what you're putting in it. Spend some time learning about this stuff, then decide what's best for you.
Cheers, and have fun