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?