Undergraduate research assistants often earn a stipend or an hourly wage, whether they work during a defined period of the summer or during the academic year. There are many possible funding sources. Some institutions offer internal grants for student-faculty research.
Beyond monetary compensation, there are many curricular structures that let undergraduates do research for credit. Your institution may award credit for directed research, independent studies, senior thesis, capstone projects, or undergraduate seminars. At some institutions, undergraduates are permitted to enroll in masters-level courses with a research component.