I went on a diet when I was 13. It was medically supervised up until a point and basically there were three rules.
1. Eat less than your body needs to maintain weight
2. Exercize to burn additional calories
3. Plan your meals so your nutritional needs are met
Usually they say to lose weight at a healthy weight, take in 500 calories less than you need to maintain. That can be hard though especially if you haven't dieted before. The best thing is to cut 250 cals-300 cals from your usual diet (have 1,700 instead of 2,000 for example) and then to burn the rest through moderate exercize like walking or swimming. You don't have to starve yourself and if you do it backfires and can cause big problems. You don't have to go crazy and exercize all day either. Walking 1 mile burns about 100 calories and takes less than 20 minutes. Lifting small handweights can build muscles in your arms and burn up calories too. Or go swim laps for free or very cheaply at your community pool or YWCA. It's really easy.
Some diets will tell you not to eat carbs, not to eat fat, etc. Forget it. There are also no good or bad foods, just keep everything in moderation. Once you've figured out how many calories you're going to eat, keep track during the day and make sure you're getting 20-30% from fat, 20% or so from protein and the rest from carbohydrates. It's ok to have a cookie or some ice cream as long as you don't go overboard. Balance it out with some healthy fruits, whole grain bread or something else good for you. If you do eat more than you wanted, make up for it by going for a 30 min walk or doing some situps or eat a bit less the next day. Also, taking a multivitamin and a calcium tablet, plus any other vitamins your doctor tells you to, will keep you in good health and stop you from having cravings. Drink lots of water, that helps to. That's all there is to it.