I've gone to High School with this girl but never really talked to her that much. Now I am in college and turns out she is also going there. How would I be able to get into a relationship with her?

Ask her out to a movie or to lunch or even just for coffee and get to know each other a little bit. If that goes well, ask her out for a second date.

All the advice you will get on all the websites you visit will boil down to: Talk With Her. Not to her, not at her, WITH her. Get that one figured out and you're all set.

WOW! I see a lot of 'How do I date' someone I don't even know. Now you are asking 'How do I get into a relationship' with someone you haven't even dated yet. Both are mind boggling. You get to know someone first.
Hi Jill, do you remember me from high school? I'm Jack.
How do you like college so far?
What courses are you taking?
Want to go for a coffee tomorrow (or the next day, or the next)? Don't say 'sometime' because then she doesn't know when or what to do next.
You look nice in that blouse. (I like your jacket, shoes, hair that way, necklace, anything!)
Do you go home for holidays? Maybe we can share expenses?
ETC
ETC
ETC

Forget a relationship, talk and find out if you like each other first.