The thighs, hips, stomach and waist are the main areas called the core, though the core also includes the lower back. These muscles can be targeted individually, but they will all be worked somewhat as a unit. It is best to work the core three to five days a week.
Stomach and Waist
The abdominal muscles include the rectus abdominus, transverse abdominus and obliques. The obliques are the waist muscles. Work these together with floor bicycle crunches. Your legs will also get some work as well. Lie on your back with your knees bent and your hands behind your ears. Lift your knees off the floor so they are over your hips. Crunch your shoulders off the ground and twist toward your left knee. Extend your right leg straight at the same time. Now, twist toward your right knee and bring your right knee back bent. Also, extend your left leg. Keep alternating twisting your shoulders and "pedalling" your legs. Each twist is considered one rep. Work up to two sets of 30 reps.
Thighs and Hips
The thighs and hips can be targeted together with side lying leg lifts. These will also secondarily work the abdominals. Start by lying on your right side with your right arm extended overhead on the ground. Bend your knees and stack your left leg on top of your right. Place your left hand on your hip. Lift your left leg off the ground, but do not allow your hips to roll forward or backward. Squeezing your abs and glutes will help you stay straight. Work up to two sets of 20 reps per side. Do both sides equally. You can straighten your legs once you can easily do 20 bent leg lifts. You can also add ankle weights to make this more challenging.
Do these exercises together in a single core workout. Do them three days a week with one or two days in between. Once you have mastered these exercises, hire a personal trainer or take a Pilates class to learn some more core exercises. You will also want to incorporate some low back exercises into your routine. Then you can start doing more than three days a week if you want, but alternate the exercises so you are not doing oblique targeted exercises like side crunches, for example, two days in a row.