If you have decided to go vegetarian, please read up on the topic so that you still manage to get the vitamins, minerals and proteins that you require. (There are no B12 vitamins in a vegetarian diet.)
A vegan further eliminates both dairy and eggs.
These are the combinations of vegetarian foods that will form a complete protein when eaten together, or within several hours of each other;

dairy + grains e.g. yogurt and granola, hummus and pita,
rice pudding — (rice and milk)

dairy + legumes e.g. refried beans and cheese

legumes (beans, lentils, peas and peanuts) + seeds
(sunflower, pumpkin, sesame etc.)

legumes + nuts e.g green beans with toasted slivered almonds

legumes + grains e.g peanut butter and whole wheat bread,
beans on whole wheat toast