Push ups along with pull ups are one of the main strenght developing exercises, they're so simple, yet effective. I'll explain what to do, and what not to.
Push-ups! Push-ups are great for your chest and shoulders. I think it's one of the most hated exercises, though, second is pull-ups and third is sit-ups.
If you can't do a single push-up, don't worry, there are many variations to help you build up your strenght up for a pushup, and more. You can use a bench, or the side of your bed to do push-ups you can also use a chair, or the side of your bath, if all fails, or you're too lazy to go somewhere (that'll be fixed soon) do them on your knees. Your hands should be at chest level, shoulder-width (palms at your shoulders, but chest level) and your head should be tucked into your neck and level with your butt. If I were to take a photo and draw a line through your body, your body should be as straight as the line.
Now, it is very important to activate and let your core (abs area) work. It'll help you, and make your core overall stronger. This exercise trains the triceps, shoulders, chest, traps, upper abs (not only completely) and it can also train wrists and fingers.
When doing push ups, it's important to keep your form as described above, and it's also important to not do them on your palms. Yes, that's right. Not on your palms. You should use your knuckles (fists) instead of your palms. Doing push ups on your palms will put a lot of your bodyweight onto your wrists in a not very well good manner. If you were to do push ups once a month, that wouldn't be a problem, but since you're going to start doing them often (throughout the day) you must use your knuckles. Using your fists on the ground might hurt the first few times, but bear through it, or go do push ups on the carpet. While using fists, you'll also be able to go down a little farther, meaning you'll have to hold yourself up from plopping to the floor harder than with normal push ups, which is great for getting a little bit more out of push ups.
Do negative push ups too. What you do is, you go/lay under a bar holding yourself with your arms extended, and pull your chest up until it touches the bar, basically, a push up, only it's backwards and you're pulling yourself up. This one is important to do, if you are only going to do push-ups without these, you are not going to develop as much pushing power as you would of otherwise, and you're going to start having trouble with your rotatory blades. You should be able to do the same number of these as you do of push-ups.
There are many variations of push ups, too many to write them all here, but the basic one is plenty, unless you want to train your shoulders more, or your triceps.