Here are some tips that can increase your chances to participate in research with your professor:

• Google your professor, know about your professor and what he or she is well known for.
• Make sure that you receive recent information about what research your professor is currently working on.
• Show an interest in your professor's research by asking him or her about it.
• Expresss your interest in working with your professor if he has any position available at that moment or in the near future.

-- From Juan Villegas