how much

It varies between chapter. To get a better estimate, google the University of Kentucky Recruitment guide for 2017. You will receive a guide for 2018 this summer.

Recruitment alone is like $50 to register and I think it was more to actually do it(? -it's been a couple years lol) Plus if you actually want to get IN to a sorority you'll need to buy nice clothes and sandals (designer stuff even).

Then it's gonna be thousands of dollars over four years for dues alone. You have to pay for tshirts, some events you're required to attend, pins, outfits for GreekSing, random stuff like matching buttons for all the girls... Then there's the expenses related to recruitment (from the actual recruiting side) - you have to wear nice clothes that match all the other girls' each day, so basically buying like six new outfits every year. You have to have your hair and nails done professionally.
Also, you better not ever be late or miss a chapter meeting (they're like 1-2 times a week) or a mandatory planned event cause they fine your ass like grass. Some also fine you for not having a high GPA or not studying a certain number of hours in the house every week.

Once you're out of college, most sororities still expect you to pay nationals dues every year to remain "in good standing".

Go for it if you think it would be worth that money to you; I just know that I personally would not have joined my sorority if I had been given an honest and transparent idea of how much it costs. I pay for my own tuition too, and I thought it was just gonna be dues. Wish I'd known how much else goes into it.

There are surely paid, overseas posters on greekrank today with poor grasps of the English language and spelling rules. No student on summer break has time or inclination to be on greekchat right now, so greekrank pays people to post here. Nice try.