My wife was a vegetarian for years prior to having kids. I can offer some advice:
First off, find out why they want to be vegetarian. Do they feel that meat as a main meal is wasteful? Is it for health reasons? A moral or religious obligation? This will determine how flexible they are (i.e. are trace amounts of animal foodstuffs OK, do I need to up our game on healthy eating in general?)
The good:
1. Vegetarian food is cheap if you cook it yourself. Base your meals on staple items like rice, lentils, beans, and in-season vegetables.
2. Food safety is easier to deal with. A week-old vegetarian curry is less likely to get dangerously nasty than a meat-based dish.
3. Most vegetarian ingredients are available in a shelf-stable form.
The bad:
1. Meat is a seasoning in and of itself. Get comfortable starting out meals by frying up an onion, adding garlic, and using veggie bullion and spices.
2. Your options for protein are limited, especially if she doesn't do eggs. Lentils cook quickly, and canned beans are also an option. Dried larger beans can be cooked quickly in a pressure cooker.
3. Is cheese or yogurt OK? If so, use these to cream up the meals. If not, this is harder to achieve. Hummus is a good protein add-on, and can add creaminess.
4. Fake meat products. These are often expensive, refrigerated and not delicious. I'm not a fan of fake meats. Consider mushrooms, (Portabellos, Criminis, etc), eggplant and other items instead. The one exception: freeze-dried TVP (textured vegetable protein) is an amazingly good ground beef stand-in.
We made a lot of curries, chilis, rice bowls, bean casseroles and the like. Good luck!
Arclight