Some people lose weight on a vegetarian diet, and others don't. It's about the choices you make for a healthy lifestyle, combined with whether your body likes a vegetarian lifestyle.
Many vegetarians in the U.S., Canada, and Europe eat eggs and dairy in addition to plants. They are called ovo-lacto vegetarians. This is the most common type of vegetarian in the West.
Ovo vegetarians eat eggs but not dairy; lacto vegetarians eat dairy but not eggs. Vegans eat neither eggs nor dairy, and strive to avoid contributing to other types of animal exploitation in their lifestyles as well. (That includes lifestyle choices such as purchasing cosmetics tested on or containing animals, buying new leather products, most silk, attending circuses that use animals for entertainment, and buying pets from breeders, among other choices.)
In some other regions of the world, especially in India and surrounding countries, eggs are not considered vegetarian. Most people who consider themselves vegetarian in India (or whose families are from India) are what might be called lacto vegetarians - those who consume dairy and vegetables, but not meat nor eggs.
There are also people who eat fish but no other animals. They are not vegetarians, though some do use the term. A more accurate term for this lifestyle would be pescetarian.
For best health, I recommend eating whole foods, as close to the plant as possible. Avoid fake foods like frozen veggie burgers, things that come in boxes or pouches, and anything that contains processed soy, corn, sugar, and especially fake sugar. Make your meals from scratch using whole, unprocessed ingredients. Eat as many green leafy veggies as you can, plus lots of other veggies and fruits. Exercise at least a little every day, and vigorously at least three times a week. Incorporate both cardio and weights into your weekly exercise regimen.
Treat yourself to a little good quality dark chocolate now and then. It's good for your happiness level and believe it or not, a little dark chocolate is good for weight loss! But keep in mind where it comes from - some chocolate is traded fairly and some cacao farmers receive a fair wage for their work. But most commercial chocolate is made from cacao sourced from plantations where the workers are not paid adequately for their work. So choose your sources wisely! Good brands local to where I live are Taza (in Somerville, MA) and Rakha (in Brooklyn, NY.) There are probably good, ethically produced brands near you too!
Check out some good cookbooks and websites for healthy, whole foods-based recipes. www.101cookbooks.com is a great website to get you started. How To Cook Everything Vegetarian and Veganomicon are great books to have on your shelf. Anything by Madhur Jaffrey is fantastic too - I love her book World Vegetarian best of all. Alicia Silverstone's Kind Diet is also a good book, believe it or not, and a good resource for getting started in a more compassionate way of approaching food.
Good luck in your new vegetarian lifestyle!