Types of Push Ups
The basic (classic) push up is done starting in the initial position by placing your hands on the floor slightly wider than your shoulder width, arms straight and supporting your body on the toes or the balls of your feet. To maintain the proper form, it is very important to keep your body straight from your heels to your neck, without dropping your head down. From this initial position you bend your arms and lower your body until it almost touches the floor and then push yourself back up to the initial position.
By varying the position of your hands you can focus more on specific muscle groups. The narrow position with the thumbs and index fingers of your hands touching (forming a diamond) will mostly stress your triceps. While the wide position will put more emphasis on your chest muscles.
You can do push ups on your knuckles or fingers or using push up stands or yoga blocks. All of these will increase the range of motion and the difficulty of the exercise.
The level of difficulty can be further increased by elevating your feet (e.g.: placing them on a bench or an exercise ball), or by doing one handed push ups, or even doing push ups in a hand stand.
On the other hand, if you find it difficult to do even one push up in the classic position, you may try doing them on your knees, or, alternatively and preferably, by placing your hands on some elevated support (e.g.: bench, table, wall etc.) Doing full body push ups on an elevated support is better than doing them on your knees, because you get used to the correct form from the very beginning and you also engage more muscle groups.
Also, placing your feet together or putting one leg over the other will increase the level of difficulty; while putting your feet at shoulder width or even wider will make it easier for you.