I'm a college student who spends a lot of time hanging out in the library/ lounges/ cafes. Do I need to ask permission to sit at a table with a cute girl I want to approach?

Dude, I'm not the best at cold approaches like this, you gotta just be like 'fuck it I'm doing it'. Especially if it's a large table made for like 4 people. Slide in casually opposite her, NOT beside her, and run your opener. Asking for permission is a DLV communicates lack of confidence/authority/etc. Remember the three second rules. The more you sit around at the table beside her wondering what you're gonna say, the more likely you are to fuck up. The fact that you sat down for a while and then decided to open her instead of opening her right away is a DLV also. I get blown out many times cause I get approach anxiety and don't follow the three second rule.

If she's with someone (or a group of people), it's a different story. Open the group, talk to her friends, neg her, etc. Just mask your intentions until you win the favour of the group. Then isolate your target and run your game accordingly. Read posts about group sets for more information, I'm a newbie at this shit too.