How soon can I exercise after I've eaten? How many minutes or hours after I eat would be considered safe to exercise?

Depends. Exercise will slow the intestinal transit time, which can lead to symptoms of pain, bloating, reflux, gas, etc. How soon one can eat after exercise will depend on quantity of food, alcohol consumption, and quantity of food. A safe rule of thumb would be to wait 1 hour after a light meal, and 2 hours after a heavy meal.
Try before eating. Exercising first thing in the morning, before you eat anything, will cause your body to tap into fat stores for energy as your carbohydrate stores will be expended overnight. Increased use of fat for energy will help you create a leaner physique. Further, the calories you eat after the workout will be deposited usefully into the muscles and liver for energy, rather than back as fat stores.