That's too difficult of a question to answer. You could be attending a party with several girls also rushing. You could be attending an evening hanging out with the girls at home watching TV. You could be attending an event with them. She should have given you an idea of what you're doing. Dress a little bit better than you normally would. For instance, you're going to a friend's house to hang out and watch TV, so you wear jeans and a sweatshirt and tennis shoes. This time maybe you wear your best jeans a nice sweater and boots. Dress seasonally appropriate and on the nicer end of socially appropriate. More than likely cocktail attire is unnecessary, just make sure you look your best in normal every day clothing.
Then, be friendly with everyone you meet. Make sure to introduce yourself by name "Hi, I'm Mary, nice to meet you" is right. "Hi, nice to meet you" is W.R.O.N.G. Ask questions, answer questions, be generally conversational. Go with the flow. And Smile! Then make sure to send a thank you to the person who invited you if you have her contact information. Good luck!
Oh, and no more comments about the process,what you've done, how you felt, etc. here since you've said which sorority has invited you. You don't want to jeopardize your chances because something you posted was misinterpreted.
"Traveling - It leaves you speechless, then turns you into a storyteller. ~ Ibn Battuta