"She enjoys studying at the university."
Translation:Hon trivs med att studera på universitetet.
Yes, before a verb, the expression is "trivas med att":
Jag trivs med att bo i Stockholm.
Jag trivs i Stockholm.
is there much of a difference between "trivs" and "tycker om" in swedish?
Well, "trivas" does not take an object for example, while "tycka om" does. And if you are talking about a person, you can't enjoy being with (trivas med) someone you haven't met, but can still like (tycka om) him/her.
Hon tycker om påven - She likes the pope
Hon trivs med påven/Hon trivs i påvens sällskap - She enjoys being with the pope :)