There are several ways to make the change. Do whatever feels more comfortable for you. Like other types of cooking, vegetarianism can be simple or complicated, expensive or inexpensive, and use foods that can only be bought in a natural foods store or your local supermarket.
There are a lot of common recipes that are easily made veggie/vegan, or already are - spaghetti and other pasta dishes, burritos, tacos, tostadas, mashed potatoes, three bean salad, pancakes, French toast, waffles, grilled cheese sandwiches, hummus, grilled veggies, oven-roasted veggies, rice, etc. The other way would be to start exploring other cuisines or methods of cooking (go for Thai, Indian, Chinese, etc.) that exclude meat in the dishes to begin with. Some people like to try both approaches.
You could also try making the dishes you usually do and just substitute tofu, seitan or other meat substitutes for the meat in the dishes. (Most supermarkets carry tofu and often other meat substitutes in the produce section. Check the frozen section, near the breakfast foods, for veggie burgers, veggie crumbles, links, and patties.)
(info from vrg.org)