There are plenty of simple ab exercises that you can do on your own, in your house, with no special equipment required.
Most of the best exercises for strengthening the ab muscles are crunches. Crunches are exercises where you bring your body right forward, curling upwards to bend yourself into a tight V shape. There are very many variations on crunches.
One of the most popular is the exercise ball crunch, which is where you lie back onto an exercise ball, and then do a crunch slowly, without the ball moving. This allows you to keep a good crunch speed, as well as supporting your back while you crunch.
Another good method is the full crunch, where you extend out your legs and then put your hands behind your head. As you pull yourself up with your hands, push outwards with your legs. If it is done right, this will exercise both your upper and lower body.
You might also try the reverse crunch (sometimes known as a V-up), where you lie on the floor, put your legs in the air, and then instead of bending up towards your legs, you bend your legs back towards you. This has the same effect, but is less strenuous, as you are lifting less weight.