Your email to a faculty member can be make-or-break. Read more to find out WHY you need the components we suggest:

Dear Dr./Ms./Mr.,

I am a (your year) (your major) major at the UI. I am interested in learning more about research in (area of interest - Psychology, Genetics, 3D design, Museums, etc). Your research on (specific aspect of their work that caught your eye) looks fascinating. Would you have time to meet with me to talk a bit more about your work and the possibilities of getting involved in research in your area?

Sincerely/Thank you,

Your name

Year and Major
This provides a bit of context for who you are.

Area of Interest
This helps them know how your interest led you to them.

Specific Aspect of Work
Its a compliment. Their research is likely a "nerd-out" topic for them. Your interest is a compliment.
Shows that you have taken the time to understand their work.

Some students simply email everyone in the department. They usually don't get responses. This distinguishes you. Faculty want students who are interested and bring a level of excitement with them. THIS IS KEY. 

Time to Talk
Neither of you have committed to anything. Don't corner them or you by asking if you can work with them. If it doesn't seem like a good fit, at least you learned something new! 

Less pressure for both of you. There is a lot of pressure behind someone saying "Can I work on your research?" This is their livelihood. An invitation to talk turns thoughts from a formal interview to a fun conversation between people with similar interests. (Again, likely a "nerd-out" topic.)

Scope each other out. You can both see whether the dynamic between you would work well. 

Learn about the work. Sometimes things look different on paper than they actually are. A conversation helps you find out whether the work or project is actually interesting to you. More in love than when you went in? Great - make a natural transition to asking how you could get involved. Not something you want to do? Great - maybe they know of other faculty members who work on research projects more in-line with your interests.