In terms of physical activity, I think weight training is one of the best ways to lose weight. By adding additional muscle mass you burn more calories around the clock. In addition, you can have more fat on you if you have muscle underneath it and it will still look good. However, if you don't have access to weights or money for a gym membership then I understand this isn't possible. If you decide on weight training then read the stickied threads at the top of the training section of these forums.
Cardio is another great way to lose weight. I like swimming the best because there is virtually no impact on your body and it offers resistance. Jogging or bicycling is next behind that. At least 30 minutes of cardio per session is a good idea, but more is better. 3-5 days per week should be sufficient.
Endurance type exercises are also excellent. Pushups, pullups/chinups (Get a pullup bar for $10-15, it's worth it), bodyweight squats, and various ab exercises are all excellent. This should improve muscle definition, strength (To a certain point), and muscular endurance. Again, 3-5 days per week is probably good.
Diet is the single most important factor in losing weight. Check out the diet section of these forums and read the stickied threads at the top. There is a lot of good info there. Also, if you do plan on gaining some muscle mass then diet is extremely important as well.
Another thing to remember is that you should gradually work your way up to the training program you should be on. For example, take two weeks lifting very light weights at high repitions to get used to proper form and balance. If you are going to start jogging, begin by doing some speed walking and jogging for 10-15 minutes at a time. You need to work your way up. Progress is the important thing; don't expect to be doing what you would like to be doing right away.
