With regards to tummy fat, remember that there is no such thing as spot training. If areas of your body are flabby, you need to be fit OVERALL before you will see the results where you want them. You need a combination of cardio and weights to build lean muscle mass and tone, where there are sprinting intervals in your cardio sessions and you’re lifting heavy with your weights.
Here are some great demos for working out at home or anywhere without traditional equipment: http://www.youtube.com/watch?v=zK32B6H0bEw