There are all sorts of exercises that work your chest muscles. However, the chest muscles are normally worked in conjunction with other muscles, as they are one of the largest muscle groups in the body. That aside, there are a lot of great chest exercises depending on what you have available. Do you go to a gym? Do you work out at home and do you have free weights?
The best exercise for chest development is the bench press, don't forget a spotter with this one. If you have dumbbells or lack a spotter another very, very good exercise is the dumbbell chest press, - basically a bench press performed with dumbbells instead of an Olympic bar. Some say these are preferable to the bench press because of a greater range of motion and the inclusion of more more assisting muscles. By altering the angle of the bench you can target different areas of the chest, incline it to work the upper chest more, decline to work the lower part of the chest. If you have a pec deck available this is one of very, very few machines I would recommend, for the reason that it gives a good pec stretch, and has a controlled range of motion which can become for someone starting out. Also, the pec dec flys can be performed in a one armed style that focuses on developing the inner part of the chest along the sternum. It really depends on what you have access to. I mean there are dumbell pullovers, there are all sorts of flys. The basic idea to get is that there are two primary types of motion that work the chest muscle. One is a motion that pushes out in front and away from the chest. The second is the type or motion that brings something from your sides to in front of your chest. Visualize a wide hug, or imagine wrapping your arms around a tree. If you were laying down, and using weights that is in simple terms a chest fly. You can also get creative and use sandbags in place of weights if you need to.
I have a suggestion for you, and before I say it, I would like to say that I have absolutely no financial or other connection with this site, its just a great site for learning exercises. Go to www.ExRx.net and there are tons of exercises for the whole body. To go directly the chest section go here http://www.exrx.net/Lists/ExList/ChestWt.html
Dips (on the downward motion) are also an excellent bodyweight exercise. Also for bodyweight exercises, don't underestimate the pushup. There are endless varieties of this to increase the difficulty level, and or shift the focus to different muscles and parts of the muscle. Do a google search for pushups and you will find several of these. FORGET gadgets like the perfect pushup, while they make work for some, they are also a quick ticket to a blown rotator cuff for many people. You don't need it, you can do anything it can do, by altering the type of pushup your doing.
I do have to tell you, all the information I have given you here is strictly from my own experience and opinion and is not meant to medical advice. I am not a certified trainer, so this is strictly a layman's opinion. When starting any exercise program its a good idea to see your doctor first, and/or a certified physical trainer. By having a trainer show you how to do these, he can help you use proper form which can help prevent you from getting major injuries. Your chest muscle in particular can be an easy muscle to tear if you aren't careful with your form. That is not to scare you away. If you use proper form and weight, its probably safer then anything else you do in a day. If you use improper form, you end reducing your gains, end up with muscle imbalances and injuries. Don't risk it. Learn right from a trainer or trusted friend.
Best of luck to you.