As someone currently preoccupied with my out of shape pp w/ #3 core, I feel compelled to contribute.
There are many muscles involved in the core, sort of layered on each other and working together, as F said. You want to build up from the base layers because if you challenge the core with exercise that its not strong enough for, you can make is bulge more! The plank is a great exercise to engage all of the muscles in the core, but again, if the base is not there, you could be making it push out instead of pulling it in.
The most inside layer of muscles is called the transverse. It wraps around your middle like a girdle. Once this is pulled in tight, you can add muscle on other layers (obliques, abdominus recti, hip flexors...) with plank, crunches, etc. A "six pack" is the outer most layer of muscles, but has little to do with having a flat stomach (strong yes, flat no).
To strengthen the transverse/inside muscle you want to pull it in. There are a couple of exercises to do for this;
Imagine that between your belly button and back is an elevator; floor one is totally relaxed, floor six is pulling your belly button into your spine as hard as you can. Pull bb (belly button) in to floor 3-ish and contract to floor 5 100x. Do this 3-5x/day. Oh yeah, do these sitting, and make sure your posture is correct first. You should feel the muscles in your back engage when you do these. If you drive a lot, thats a good time...
Another one you could do is to suck your bb in to floor 6+ and hold for a count of 30 then pulse it in harder 10x. Relax. Do this 10x/day. I used to do these when I drove dd to and from school.
As for losing belly fat - you cant do spot exercises for this. yes diet will make a big difference, but so will aerobic exercise and strength training. meaning, running or swimming will burn belly fat, as will strength training your arms and legs, as all of these burn fat for fuel from your body
Good luck to us all