A sit up is pretty much what you remember from grade school: lay on your back, knees bent, and roll all the way up, go back down, and repeat. From everything I've read, sit-ups are frowned on nowadays as being too hard on your lower back, and most experts prefer crunches to sit-ups.
There are different types of crunches, but the basics are that you start out in a sit-up position, but instead of going all the way up you only come up off the floor a little further than the point where your shoulders are off the ground. You basically only go about 1/4 of the way up. But, you keep your back straight, your belly as tight as possible (picture pulling your belly button in towards your spine), your chin off your chest (picture a tennis ball under your chin), and your elbows out to the side to where you can't see them. Lower, and repeat.
A "full" crunch is where you pull your knees up and roll your upper body up at the same time. Picture curling yourself up into a sort of fetal position, with your tummy tucked in tight. Your elbows don't have to touch your knees, but your shoulders have to come up off the floor, and your butt should too.
Here are a few "core" moves to give you an idea of what they are like:
*The "plank" manuever: Lay on the floor on your tummy with your elbows under your shoulders (you can fold your hands together or keep your arms parallel on the ground if you like). Then, keeping your back straight, your elbows on the floor, and your body in a straight line, lift your body off the ground. The only parts of your body that should be on the ground are your elbows and forearms, and your feet. Hold for 3 counts, and slowly lower to the ground. Repeat. Don't let your body sag or arch up: keep it in a straight line.
There are variations on this, such as starting in a push-up position and then just lowering your knees to the ground and back up to push-up position.
*I think it's called "Cobra" in yoga, but basically you are again laying on your tummy, but this time put both your hands under your chin with your elbows out to the side. Lift your upper body up a little bit off the floor, hold for 3 beats, and lower. Great lower back exercise, but don't do it if it hurts!
There are tons of videos out there that address core strength and different crunches you can do. Also, muscle and fitness magazines usually run articles about stuff like that and usually post articles about it online. (I've learned what I know about this stuff from work-out vids and fitness mags, so they are great resources!)
Happy hunting!
