"She is a student."
Translation:Sie ist Schülerin.
Both "Sie ist Schülerin" and "Sie ist Studentin" are fine. Note that they're not interchangeable.
Also, it sounds more natural without the indefinite article.
German here: Both of these options are just fine, but with the article it is a little bit more formal. But just a little bit; no one in Germany will care which you choose. Most Germans usually go with " 'ne", which is the short form of "eine".
I don't think there actually is a rule for when to omit the article or not, but I may be wrong here.