Lower abdominals:
1. Heel taps: Lie on your back and tuck your heals in towards your glutes. Your knees should be pointing the sky. Crunch up your torso, and rock back and forth, touching your left hand to your left heel, and then your right hand to your right heel.
2. Leg raises: Lie on your back with your legs out straight. Keep your heels close together and raise your legs up, then lower them back down. Do not let your lower back come off the ground during these exercises to prevent injury and keep the intensity on the lower abs.
3. Flutter/Scissor kicks: These are both relatively the same exercise. Lie on your back and lift your legs a comfortable amount off the ground. The lower they are, the harder these movements will be. For flutter kicks, move each your right leg up and your left leg down, then vice versa. Repeat this for as long as you wish. Scissor kicks are similar, but involve a vertical and horizontal motion of the legs. Go to do a flutter kick, but when your right leg is lower than your left, cross it over and make a scissoring motion. Repeat on the other side.
4. Bent knee toe taps/Dead bugs: Lie on your back and raise your knees so that your knees are above your hip points and so your shins are parallel with the sky. Slowly drop one foot to the floor, then bring it back up so that it is level with the other one. Repeat on the other side.
Upper Abdominals:
1. Crunches: Lie on your back with your legs bent so that your heels are pulled in closer to your glutes. Put your hands behind your ears and keep your elbows wide. Lift the top half of your torso up and crunch in with your abs, bringing your nose as close to your knees as you can without making a full sit up. Slowly lower back down and repeat.
2. Toe touch crunches: Start in the same position you would do a crunch in. Raise your legs up so that your feet are above your hip points, or as high as you can get them (you can bend your legs as well if you have tight hamstrings). Crunch up as if you were trying to reach your toes or touch the ceiling. Lower back down, and repeat.
3. Sit ups: A classic exercise. Lie on your back with your legs bent and with your heels on the ground. If you'd like you can have someone hold your feet or slide your feet under something like a couch or some gym equipment to make it easier. Crunch up using your abdominals until your chest is at your knees, then lower back down slowly. Repeat. (these are different from crunches because you come all the way up)
4. Tuck crunch: Lie down on your back. Keep your shoulders and legs off the ground for every rep. Tuck your knees in to your chest and bring your arms around to your rear while crunching up. Slowly kick your legs back out straight and your arms back behind your head as you lower both almost so that they touch the ground, then repeat.