You can find different ab exercises in these ab exercise pages. Most of them can be done at home, although some of them may need some equipment to do. Basically every ab exercise worksout your whole abdominal area, but different exercises target more on some areas like lower abs. Remember to execute these exercises in controlled motion so that you don't cheat. With rocking motion or some other cheating method you are just fooling yourself and can't expect any results from your exercising.
As most of these ab exercises can be done at home, usually the harder ab exercises need some equipment like incline bench. Using weights also helps you to get a harder workout when these exercises start to feel too easy. If you already go to your local gym, it is easy to make your ab workouts harder by using dumbbells, weight plates or some other weights to give you more resistance. Most gyms have also basic ab exercise machines so you don't have to worry about that.
To get more work to side of your stomach, which will help you to make your stomach flatter, add a twist to your exercises. Almost all of these ab exercises can be done with twist, execute the part where you raise yourself but at the end of the movement twist your body so that your left elbow for example touches your right knee.