Pushups are awesome. They don't take any space, they work out a bunch of muscles, and they literally only use your own body for weight. The best part? They're easily modified and performed in a variety of ways that can add variety and challenge to your workout.
Let's start with the traditional open handed pushup:
All you have to do is place your hands parallel at about shoulder width, and lower and raise your body. That's the entirety of the motion. A few things to note:
1. Keep your back straight. Lots of people arch their backs as they get tired. That's not good for you or for the quality of the workout.
2. Try to lower yourself as close to touching the floor as possible.
Can't knock those out yet? No problem! Rest some of your body weight on your knees, and do them in that position:
While this doesn't quite give you the same workout, it's a good way to build up the upper-body strength you'll need to do a full regular pushup.
I don't buy into the whole "don't do modified exercises" argument because I think it discourages people from doing anything at all. Better to modify and build up than to get discouraged early on and end up doing nothing in the long-run!
So, you've knocked out your first 10 and you're wondering, "what's next?"
Easy, 100! Do a build-up training like at this site: http://hundredpushups.com/ and increase muscle and endurance. Even if you only add 10 or 20, it's still a good way to set some goals as you improve your fitness.
Diamond pushups! Good for triceps, though some say they're harder on the wrists and shoulders. I don't make them a big focus, but I don't entirely avoid them.
Another thing to do is to vary your arm width throughout the workout:
By doing so, you can target different muscles in different ways.
You can also do incline or decline pushups by putting your feet or hands up on a chair or box. Eventually, you can even work your way up to the handstand pushup (a favorite of mine!)
I especially like handstand pushups because they develop balance, require core strength, and really work out your arms!
Regardless, if you aren't doing pushups, they're a great addition to any workout routine!