One way to improve your odds is to find an area that interests you, see which professor is working in that area, and then come up with a short proposal of something you might do in the area.
Individual initiative is important in approaching faculty to ask about research opportunities.
Ask your undergraduate faculty advisor for direction. The Office of Undergraduate Research website contains links to many Berkeley research programs for undergraduates. The spring poster session will illustrate how Berkeley undergraduates are performing research that benefits society as a whole. The second annual EECS Undergraduate Research Poster Session focused attention on the research contributions of undergraduates and gave students an opportunity to display and discuss their work. After the session, attendees enjoyed ice cream courtesy of Cisco Systems.