Diet is probably a big part of why that happened in the first place (congratulations, by the way
) so diet is the first place to start. What does your diet look like right now? You don't need A
diet, rather a permanent change in your eating habits. List an average day's food - what you eat, how much and when. Also provide your stats please (height/weight). It will help to identify what your caloric needs are.
As for exercise, cardio is good for burning calories (running, biking etc), but putting on some muscle tone will be important for raising metabolism and overall health. If space is a problem, consider resistance bands or removeable plate dumbells. They are pretty inexpensive and easy to store in a small area. Or just use your own body weight - pushups, jump squats, pullups, calisthenics etc. Maybe even somehting like a Tae Bo video that is a little higher intensity, but structured and easy to follow. Just some suggestions...