It started when she hooked up with someone at a party.
The phrasal verb hook up with someone can be used a slang expression meaning to have sex with someone, especially someone you just met, or someone you only stay with for one night.
Sarah asks Emily if Emily is going out with anyone.
The phrasal verb go out with can mean to go out on a date with someone once, or it can mean to be in a relationship for an extended period of time.
My last boyfriend and I didn’t hit it off right away – I only started to fall for him after we went out a few times and I got to know him better. First, Emily says it looked like the guy was hitting on Sarah.