Believe it or not, opportunities are more readily available than you think. Most research opportunities in labs at UCLA are only a question away. All you have to do is ask a professor to research in their lab and they'll tell you whether they can take you or not. Your first choice isn't always for sure so don't be let down if you get turned down, just try try again.
HINT: Professors like volunteers. If you're more in the market for experience than money, you're more likely to get research opportunities. Also, sometimes, labs just fill up.
Research Opportunities at UCLA