Conducting research within the structure of a course allows you to work under the guidance and support of a faculty member and receive academic credit for your project.
Students with a major in the Department of Slavic, East European & Eurasian Languages & Cultures take Slavic 191TA-B-C and work with a faculty advisor to write a senior thesis on a topic of their choice. All of these students present their research at the department's undergraduate conference and many of their projects go on to be published in the undergraduate journal.
The UCLA Quarter in Washington Program includes a research development seminar (M194DC), in which students produce an original research project under the supervision of a professor.
Most departments offer research courses (99s and 199s), which allow students to receive course credit for an independent research or creative project under the guidance of a faculty mentor.
Most majors at UCLA have Departmental Honors Programs which include a research project component - each department has different requirements so check out the website of your department.
The Luskin Center for History and Policy hosts a summer research institute to equip students with the skills to conduct historical research and policy analysis. Students interested in topics related to history or policy in the former Soviet space should consider applying to this institute.
The Undergraduate Research Portal lists undergraduate research projects with UCLA faculty in all disciplines. You can search for research opportunities both on and off campus, or create a profile that faculty can find when looking for student researchers.