This is intended for those who not only aren't vegetarians, but aren't terribly familiar with them either. I am not a vegetarian myself (I'm too Texan to give up my steaks, thanks), but I have vegetarian friends of most sorts. This isn't necessarily a post on being frugal, but once you know a little more, you can make lower cost choices.
OK, your brother's just announced that he's bringing someone with him to dinner this weekend, and oh, by the way, she's a vegetarian. Once you get over the shock that your brother is actually bringing a (possible) girlfriend to meet your family, don't panic at the idea of having a vegetarian at your table.
The first question is: what sort of vegetarian is she? Many people are very surprised to discover how many shades of vegetarianism there are. The first basic level, in general, is people who simply don't eat red meat (i.e. no beef, pork, lamb, or other mammal). They will eat poultry, fish, eggs, and dairy. The next level of vegetarian is someone who doesn't eat any meat but will eat dairy and may eat some eggs. Beyond that is someone who eats no animal products whatsoever, including dairy and eggs (called a vegan). Then fructarianism (or fruitarianism) are people who eat only fruits, nuts, and seeds. The most extreme form I'm familiar with are jainists, which is a religion so opposed to violence that some of them only eat foods that can be gotten without harm to a plant. If your brother's girlfriend is one of the last two groups, you might suggest going out to eat someplace that she finds acceptable. But the rest are easy enough to work with.
Oh, and most of those levels divide into two "camps": those who are vegetarians for "health" reasons, and those who object to animal products as cruelty to animals---an "ethics" vegetarian.
At the "no-red-meat" level, just serve a chicken or fish main course and watch out that you don't use things like beef broth. At the next level, consider a main dish that relies heavily on cheese and/or eggs. Pizza or homemade macaroni and cheese or a pasta dish without meat in the sauce. One caution, though. If she's a "health" vegetarian, cheeses aren't a problem. If she's an "ethics" vegetarian, forego the cheese, they'll only eat cheeses made in certain ways, and you'll find those expensive and risk making a mistake.
With vegans, you're getting into somewhat trickier territory, but you can still produce a good meal that everyone can enjoy without buying exotic foods. If she's a "health" vegetarian, you can probably also serve a dish with meat for the rest of the family if you fear family riots over a completely meatless meal. But there are lots of common, delicious foods that a vegan will enjoy. You can buy vegetable broth and use it to make mushroom and potato soup, or some other sort of vegetable soup (these usually need more salt that regular meat broths). Gazpacho. All sorts of salads, complicated and simple (just be careful of the dressings). Vegetable side dishes (baked potatoes, steamed carrots). Brown rice or breads (but make sure they're made without eggs or butter). Desserts can be fruit-and-nut salads, apple crisp, eggless-and-butterless pastries, and some fruit ices (make sure they don't include dairy).
Avoid most pastas (they're made with eggs), but there's a small grain-like pasta called couscous that is delicious, fast and easy to cook up, and not very expensive if you buy it in bulk (this is one of my favorites when we need a quick starch with a meal).
And just as a matter of perspective, meatless doesn't mean deprivation: when I was a kid, we had a huge garden (a full acre at times), and during the summer when we had huge amounts of fresh produce and it was too hot to cook much, our suppers were often platters of fresh produce with bread and butter and some kind of cooked grain---fresh sliced tomatoes, cucumbers, canteloupe, celery, carrots, steamed corn on the cob, beans, breaded fried squash and okra, cabbage, a huge salad, mashed potatoes or sweet potatoes, and dill and sweet pickles. There usually was a small main dish with at least a little meat (often a leftover casserole), but not always. And once the weather cooled, we had many suppers that were big pots of bean soups or bean casseroles with corn bread and a salad with no meat at all. I doubt my parents had even heard of vegetarianism then, and there were many nights we had meat-heavy meals. But the produce-heavy summer suppers were just what you did when you had a garden, and my mother's bean soup and corn bread were delicious. We certainly didn't consider either of those suppers a deprivation: I think we ate much better than most people I knew, and some of my best meal-time memories are of the fresh summer produce on the table.