A previous post dealt with how to manipulate the difficulty of the pushup by elevating the limbs. In this post, I'll tackle how to change hand positioning when doing the pushup. Such a simple change can dramatically modify where the stress of the pushup is transferred to. The ease or difficulty will depend upon where you are strong or weak in your body.
The standard pushup sometimes gives people trouble with their wrists. One simple way to alleviate that is to perform the pushup on the fists rather than the palm. This variation has several benefits. In addition to straightening the wrists, it adds a couple of inches to the range of motion if you so chose to do. If you're involved in combat sports, pushups on the fists will help you hard-wire the proper fist form. You could even do these with handstand pushups.
If you want to strengthen your forearms and fingers, you could do pushups on your fingertips. These are somewhat difficult to do but the strengthening benefits of them are immeasurable. You may want to warm up first by doing some light stretching.
These first couple of variations deal with how your hands contact the floor when pushing up. You can also move your hands to change the muscular emphasis of the pushup. When the hands are moved closer together, or even overlapped or formed in the shape of a triangle, the emphasis is moved to the triceps.
As you move past shoulder-width apart, you will place more of the emphasis to the shoulders. These are great if your elbows are somehow compromised by weakness or injury. Where on the shoulders depends on where you want it. You could keep your fingers pointing foreward and keep the stress on the sides of the shoulders. Pointing the fingers outward will place more of the stress on the back of the shoulders.