The basics of weight gain/loss is how many calories you eat per day vs. how many you burn. There are about 3500 calories in a pound of fat. When you eat, any left over calories get stored as fat. That's the simple way of looking at it. Find something that works for you, which should include a change in diet (caloric intake) AND exercise levels.
Most successful weight loss stories involve some kind of exercise regimen. Not only do you burn a few hundred calories per workout, but your muscles metabolize more calories when at rest when they're stronger. You burn roughly 1500 calories a day just to keep your body going (if you live a sedentary kind of life) and probably around 2500 if you're active. So, if you're sedentary, and you start working out, your base metabolism will start to rise (your body will start to burn more calories per day on its own), AND you'll also burn the extra calories every time you work out. Well, a few hundred calories may not seem like a lot per workout, but it adds up over months, and you'll lose weight and feel better. Be sure to include some strength training as well as aerobic exercise. Oh, and stretching is super-important for how you feel, too, so be sure to do that after every workout.
Changing to a vegetarian or vegan diet won't help you lose weight. Sure, some people believe that there are health benefits to it, but if you're eating 3000 calories per meal of pure vegan goodness, you're still going to gain weight. The problem is portion control. If you feel as though you need to eat a lot to feel satisfied, you may have either a psychological or physical imbalance, or you just might be an American. What I've had success with is a tip I learned from a relative who dropped over 100 pounds. He felt as though he had to eat a LOT of food every meal so that the hunger would go away, so he'd eat the volume he needed in lower-calorie foods (carrots, broccoli, celery, etc...), and have a little bit of other food with it. He was getting the volume his stomach "needed" to lose the hunger pains, and because he was eating healthier, that amount got less and less. If your body doesn't get what it needs, then it might tell you that you're hungry when you aren't actually--it's trying to get the nutrients it needs. Sometimes, your body is just dehydrated, but it might be misunderstood as hunger.
In the end, self-control, dedication, and motivation are the biggest factors to success in losing weight. If you don't have those, you won't be able to stick to a lifestyle change and see it through. Hope this helps!