The parts of a simple introductory paragraph are a hook sentence, an introduction to the topic, and a thesis statement. Since your essay is about vegetarianism, I would start with a quote or statistic about vegetarians. This could be something like, "Studies show that 40% of vegetarians live longer than meat-eaters." or something like that. Introducing your topic is pretty self-explanatory. Just talk about what it means to be a vegetarian. You're probably familiar with writing a thesis statement. A thesis statement is a fact statement about your topic and summarizes the main point of your essay. A example of this could be (depending on your viewpoint) "Vegetarians are ultimately healthier that meat-eaters" or "A vegetarian diet is a healthier and makes one happier than dieting and consuming meat.".
Hopefully this helped a bit! Good luck on your essay!