How to apply for a research internship at the master's level? I'm a master's student doing research in the field of the cognitive psychology of language and I would like to do an unpaid 4-month research internship in a different university. I am preparing cover letters to send to different professors within whose projects I would like to work. I want to include in my cover letter a description of what I plan to do during my short internship, so I want to know what research interns usually do. How can they contribute to an existing research project?  Also, can I say that I want to learn how to use a specific research technique (like for example a neuroimaging technique) even if I have no experience with it?

Do you have any general advice on how to best ask a professor to accept me as an intern within their research project?
Networking is key--check out F'x's answer to this question. Find people in your university who are willing to recommend you to the other researchers in the field, whom you would like to work with. Take advantage of the connections your faculty members have developed.

Then write a killer cover letter. aeismail notes that a compelling 'cover letter' email was the only reason he even considered an individual for a research internship. Research the PI and tailor your letter to his/her interests and current project.