Undergraduate research projects can be undertaken for credit or for pay (See the rules from the Office of Undergraduate Education). Your needs and the availability of research funds will determine which option is best for you.
If you are interested in doing an undergraduate research project in my group and if your combined CS and Math GPA is greater than 3.4, then send email to trink (AT) cs.rpi.edu with the following content:
I will review your materials, contact your references, and then contact you.