Not only is there alot of paperwork involved, but as a student, your most likely option would be to teach english. Even giving conversation classes.
Just as foreign students going to the US to study have a hard time getting something part time unless its a part of the program, your chances are slim to none.
I'm not trying to be negative, just realistic. Check out other posts that have to do with working (everything from student to professional is discussed!)
Good luck!
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Madrid!