Because the information on VeganHealth.org can be so long and complicated, this page is devoted to making things as simple as possible for vegan teens. Here are the most important things to know for most teenage vegans:
Drinking one cup of soymilk fortified with vitamin B12, calcium, and vitamin D each day can go a long way towards giving you the nutrition that might otherwise be lacking in a vegan diet. And if you were to drink two cups, you would really be covered.
A daily supplement with vitamin B12, vitamin D, iodine, iron, and zinc is also a good idea. There are many available -- you can get one at any grocery store. Some might not be completely vegan and if you don't have the time or money to worry about that, then you shouldn't. But if you do want to have a completely vegan multivitamin, Deva Nutrition has a good one.
It's a good idea to crush up any multivitamin (and eat it with something to disguise the taste) before swallowing, to make sure it is digested properly.
You should get some omega-3s in your daily diet. A tablespoon of canola oil or a teaspoon of flaxseed oil on some bread is a good way, and walnuts are also a good source.
Other than that, it is important to eat yellow and green vegetables daily for vitamin A, iron, and calcium, and to eat legumes for protein, zinc, and folate.
It is a good idea for vegetarian teens, and especially teenage girls, to make sure they eat a food that has a large amount of vitamin C with at least two meals each day, especially meals with legumes. This is because vitamin C greatly increases iron absorption of plant foods. Some foods that are high in vitamin C per typical serving are orange juice and grapefruit juice (80 mg per cup), oranges (50 mg per small orange), broccoli (50 mg per 1/2 cup cooked, chopped), strawberries (85 mg per 1 cup of whole berries), grapefruit (40-50 mg per 1/2 fruit), yellow peppers (70 mg per 1/4 cup chopped), and red peppers (50 mg per 1/4 cup chopped).
More information on all these topics can be found starting on the daily recommendations page.
Also see the booklet Vegan Nutrition for Teenagers, by Reed Mangels, PhD, RD (PDF) from the Vegetarian Resource Group.