OK.
First of all I have no experience in advising Mums who are returning to exercise after c-section so please check with your GP/use your judgement (and I don't know how long it is since the birth - congratulations by the way!) before doing any of the following...
Well, just sitting on it to start with, for 15 minutes or so at a time, will help your 'core stability', which includes using the deep abdominal muscles and the pelvic floor that are difficult to reach via the usual stomach crunches/curls. I used to watch the news on it - the timing was about right!
Important stuff though - you need to sit on it so your knees are about at right angles (you may need to inflate or deflate the ball a bit) or your pelvis is a bit higher than your knees - definitely not the other way around.
Place your feet flat on the floor, and make sure your weight is a little forward of the centre of the ball - that helps you keep your back upright, and avoid slouching.
In order to challenge your stability (and therefore the muscles needed to keep you stable) once you feel secure just sitting on it, try very gently lifting one foot off the floor, just an inch or so at first, without rolling completely onto the other buttock/letting your pelvis tip for balance - harder than it sounds!
If you know how to do a really good, effective tummy curl, you can do those on the ball too - start from the relaxed, comfy sitting position, knees hip-distance apart, then slowly walk your feet forward so the ball rolls forward and your bum and lower back are supported by the ball when you're leaning back. While doing slow, concentrated tummy curls you'll also be challenging core muscles, buttocks and thigh muscles.
I'd start with that - let me know how you do and I have lots more to pass on!
Found this:
youtube link and there are a lot of other swiss-ball videos around - but please be careful! Almost none are post-natal specific and certainly don't seem to be taking a c-section into consideration. But, they may help you to get into some of the basic positions better than trying to read instructions from mumsnet!
You also need to be doing some light cardio work if you've got flab you want to shift. Tummy exercises will hold the flab up better and pilates in particular will improve your whole posture, but while toning exercises can improve your ability to burn fat it's the aerobic exercise that really shifts it. So a bit of sling/pushchair power walking (when you're fit and well), some swimming, anything to get you a little out of breath and warm, three times a week or so, will help.
HTHs