The difference between the classic floor crunch and the exercise ball crunch is leg usage. On the floor abs crunch the legs often are used to swing a little bit to make the proper crunch; on the exercise ball almost the entire crunch process lies on the abs.
Sit on the exercise ball a bit forward from the center. Position the legs in a 90 degree angle to the floor. Now place your hands behind your neck and start making a classic abs crunch with your upper body moving towards the stomach.
The trick in these exercises is that you have to maintain balance on the ball as not to swing side to side and eventually fall down. A great thing about preserving the balance is that the abs are those responsible for it. So not only do they make crunches, but also help you maintain the flow of the exercise in the right direction.
In the beginning you may experience balance problems on the legs. The crunches themselves will cause the feet to rise from the floor a bit and push you of balance. Some people use ankle weight straps of about 1 kilo each to put weight on the legs. It is not wrong to use them, but once you get into the spine of the exercise, remove them so that the abs will be more challenged during the crunches.
The possibilities of cab-crunch movements are the same as on the floor crunches; you can crunch form left to right in order to trigger the side abs muscles.