Yo people!
I won't beat around the bush, I'll just get to the point.

I won't say I've been gaming in college, I've just generally been talking to people, and let's just say people know who I am. About a month ago I noticed that girls were half-comin on to me. As I've never had sex nor had a girlfriend all I know is from reading about pickup online.
So there's this one girl who, when we meet, puts her arm around me and I put my arm around her. So some kind of kino quite immediately. Problem is that I don't know how to escalate from there. There are more or less always other people in the room as well. So should I just rub her back? Move down to the thigh, graze her boobs or what? And when do I go for the kiss? Tl; dr, how should I kino escalate in this position and how should I do the transitions in a non-shitty way?

This is my first "game", so I have no idea what to do at all xD
Do give me advice, it's appreciated ^^

Next time you see her, suggest that you go back to her room or your room. Then you can escalate to making out / sex from there.

Watch some instructional videos on how to get good at sex. Sex is no big deal, don't be scared homie

Constant eye contact.
Touch her a lot.
Look at her mouth.
Pull her towards you when there is a lull in the conversation and kiss her.
Then suggest you go somewhere more private (your room / her room)

All of those tips are good...

Isolation is huge though, once you get to the kissing and sexual touching phase. Don't do all this in front of people if you can help it. Get her somewhere private. She'll be more likely to be open to this stuff.