Look for these programs at colleges and universities in your area. Sometimes, even hospitals and clinics will let a bright, interested student work in a lab. A number of research grants and private scholarship funds are available from companies like Beckman Instruments and Pfizer, Inc. to pay an undergraduate working in a research lab. If your grades are good and if your project is sexy, your entire undergraduate education may be funded by companies and individuals supporting your research. Know that you'll fall, but don't give up.
Research is hard work.
Expect to put a lot of time into research. No matter how you prepare academically, it still takes time to learn how things work in the lab. It will be overwhelming at first, but you soon learn the vocabulary and gain the skills you need to become a productive member of the lab. Learn everything you can from this person, and ask about anything you don't understand. Don't be afraid to ask questions.