It varies from campus to campus and sorority to sorority. My school doesn't have houses, so there were no fees for that. Though if she's already living on campus or away from home, the cost would probably be similar with the sorority generally including some meals.
Some sororities charge dues and that covers all of your activities for the year, some charge dues and then charge for activities and events. There's also the cost of t-shirts, event favors (tshirts, water bottles, things with the event logo etc), big sister/little sister presents etc.
My sorority charges an initiation fee, which I imagine all do, and generally some type of house corporation fee, every one pays, whether the chapter has a house, you live in or out.
Then there's event clothes, but there's normally a lot of sharing with that, so it's possible to do that without spending a ton.
Dues/fees etc are always addressed during recruitment.
Is she a senior in high school, or already at university? If she's already at school, she should be able to ask any chapter she's interested in about their dues before she decides to do anything. If she's a senior, then I strongly suggest she find out about greek life before she gets to school. Some campuses have recruitment before school starts and some require women to have recommendations from an alumnae of their chapter to even consider them.
I'd be happy to answer any other questions she may have. I think greek life can be great, but it's not for everyone. It can also be that greek life on her campus isn't for her, but could be elsewhere as they aren't all the same. I volunteer with my sorority advising alumnae chapters in my part of the country.