I'm training to be one...
First thing I'd say is that firming up a tummy requires you to both get rid of the/any fat on it, and tighten/tone up the muscles beneath.
The generally accepted viewpoint is that you can't 'spot reduce', meaning that you can't do exercises to get rid of fat in a specific spot: rather you have to work on getting rid of fat in general and it'll come off from the desired area. So cardio cardio cardio and a healthy balanced diet. Make sure you eat enough (a common mistake) - www.myfitnesspal.com is great at explaining this and the need to not make your body feel it's being starved (and so cling onto anything you eat).
Together with the cardio, sit-ups are good, but they're not the only exercise. If you do them, mix it up: twisting crunches are good (fingertips to ears, reach elbow to opposite knee). Also - I'd personally avoid full sit-ups (they can harm your spine): small crunches are better. And when you do them, ensure your tummy button is sucked in, otherwise you'll build the wrong muscles.
As a PP said, the plank is also great move, as is Pilates in general (the 'hundred' (lie on your back, legs up in the air as close to the ground as you can manage without touching it, shoulder-blades off the ground, and pulse your arms 100 times), or the bicycle (similar position to the hundred but cycle with your legs, bringing opposite elbow to knee) for example): try youtube for short sessions.
You can also combine cardio moves with core strengthening ones (for example, knees lifts to the side, bringing elbow to knee). Balance exercises also work your core. Lindsay Brin's Boot Camp for Moms has a number of short core workouts, as well as a number of cardio workouts which also work the core: might be on google.
Also try side raises: lie on one side and raise yourself up on one elbow, holding your hips off the ground. Raise and lower your hips. This works your obliques.
Also, during the day, be aware of your core and suck it in! Try to get your tummy button to touch your spine as often as you remember.
Does this help?