N.M.
I'm a physical therapist and have taught the proper sit up many times. You start with the pelvic tilt. That is lay on your back and without holding your breath press your back down into the floor. If you have trouble with this lie on your back and just try to raise your head, this should tighten your abdominals so you can feel it in your tummy. Once you can do this you can progress to a crunch where you cross your arm on your chest and lift your head and shoulders just off the floor while holding the pelvic tilt. If you can not hold your back flat, your abdominals are too weak to progress to the next step. When crossed arms is easy, put your hands behind your head (but do not pull on your head so you are straining your neck). Hold each rep 3 seconds each to begin and progress to 5 or more seconds. Do not hook your feet under the couch either, this will work the hip flexors-see below for defn- in most people more than your abdominals) You can do the pelvic tilts sitting or standing too, so it is a portable exercise, that actually is good to do upright because this is the position we function in. You can also think of it as bringing your belly button to your spine. This is a beginning. You can also work the lower abdominals more by doing the same pelvic tilt and bending your knees with your feet on the bed do a march motion while keeping the back flat on the floor. Only move the feet as much as you can maintain the control of the tilt. The progression for lower abs is to do this with a straight leg (opposite bent), and then finally double legged. Each step must have the back flat down to the floor, or you are not strong enough and will only strengthen the hip flexor muscles (the ones that bring your hip up like you are going to knee someone) and this will cause your back to arch more and your tummy to hang out. (Not what we are going for at all!) Be careful with this though, you should not have back pain at all. If you do, stop.
The other responses about nutrition are important too. You really can't "spot reduce", that is slim down hips, butt, or tummy with crunches and lifts without watching diet.
There are 4 groups of abdominal muscles: Rectus abdominus (six pack), obliques (2 groups running on a diagonal each direction), and then the transverse abdominals (deepest running like rings around you corset style). Crunches work the rectus group, doing the diagonal sit up works the obliques (also done with a pelvic tilt in a slow controlled motion), and the others have told you of transverse.
Biggest key is to do them slowly and properly and hold them longer, so you will need to do fewer reps.
A bit lengthy, but this is actually one of the hardest exercises to get people to do properly. Hope this helps.
N.