What specific foods should you avoid and why?

You should avoid foods like:
ALL meats, sugars and too much carbohydrates.

Avoiding meats is obvious because if you are a vegetarian then meat will not be in your diet anyways.
You should avoid things with lots of sugar in them because sugar means fat and fat is bad. The natural sugars like the sugar in apples is good for you. But something like a hersheys bar would be a bad choice in sugar.
It's a good idea to avoid lots of carbohydrates since they have lots of calories. The carbs that have been processed or refined should be stayed away from because it is hard for your body to digest them. Examples are processed pastas, breads, sodas, candy and things refined with white flour. If you eat foods like this too much you could end up gaining weight.

What specific foods would you include, and why?

Since vegetarians aren't getting protein from meat products they have to make a well balanced diet of a variety of different foods that can balance out eachother such as: grains, fruit and vegetables, beans, nuts or seeds, a small amount of fat, with or without dairy products. (http://www.annecollins.com/vegetarian-diet-nutrition.htm)

To be more specific here are the groups of food that your body needs in order to stay healthy and keep a balanced diet.
1) Protein: soy products, meat substitutes, legumes, lentils, nuts, seeds and whole grains.
2) Calcium: spinach, turnip and collard greens, kale, broccoli, and fruit juices.
3) Vitamin B-12: eggs and cheese.
4) Iron: Dried beans and peas, lentils, enriched cereals, whole-grain products, dark leafy green vegetables, and dried fruit.
5) Zinc: whole grains, soy products, nuts and wheat germ.
(http://www.mayoclinic.com/health/vegetarian-diet/HQ01596)