Mostly plants, with an emphasis on getting enough fiber (usually from whole grains, beans and leafy greens and nuts) people with gluten intolerances and people with celiac disease are really the only ones who need to avoid wheat and other gluten-laden grains.
Low fat, but not non fat. People need to have some fats in their diet to make their bodies function properly. So some low fat dairy products (from sources where the cows are not given hormones) unless the person is lactose intolerant or allergic to milk products. Low or non fat plain yogurt with live bacteria is another good source, and you need some of the “good” vegetable oils such as olive oil and canola oil. Nuts are an excellent source of the “good fats” but because they are full fat, you need to limit your intake of nuts to a small handfull per day.
And you definitely need protein, but not as much as most Americans get with their typical diets. Here’s some info about protein intake. Great vegetarian sources of protein are combinations of whole grains/beans together, tofu and nuts. Quinoa is one of the few plant products that provides a complete protein (meaning that you don’t have to eat it in combination with other foods to get the whole protein). Egg whites are another good source of protein (unfortunately the yolks contain a lot of cholesterol and should probably be limited)
You should eat plenty of foods that are described as being nutrient dense (which rules out all junk food and most processed foods) Good sources are: berries, mushrooms of all kinds (maitake is a powerhouse), leafy greens (kale is a powerhouse), any of the cruciferous veggies like Brussels sprouts, cabbage, broccoli and cauliflower, low or fat free plain yogurt (make sure to get yogurt with live bacteria) sweet potatoes, nuts, peppers (especially red bell peppers), squash, root vegetables and tea. Red and purple fruits and veggies are temendously nutrient dense too (apples, tomatoes, beets). Your best bet is to eat fruits and veggies from the whole spectrum of colors, so that you get the entire complement of nutrients. Don’t just limit yourself to one or two veggies. Try them all!
Most people get their omega 3 fatty acids from fish, but vegetarians can get it from nuts and seeds. The best vegetarian source for omega 3 fatty acids is from ground flax seeds.You can read some info about this topic here
The way food is prepared can effect the way that the nutrients are absorbed by the body. There are people that think a raw food diet is the way to go, but some foods need to be heated to release the nutrients from the vegetable. You can read more about that here
Women, especially during their child bearing years, need to get iron. Luckily there are many good vegetarian sources of iron. You can read about how much iron men, women and children need and where to find it in your food here
If a person decides to be a strict vegan (rather than a vegetarian who probably eats eggs and milk) they will need to find vegan sources of vitamin B-12, which is readily found in animal products, including eggs and milk. You can read about vegan sources for Vit B-12 here