How do I approach a stranger.. just like that?

Very important context: I’m an Indian in India.

I live on a college campus (have been for a year), have a small group of friends and I am generally talkative a probably extroverted. However, there are some people I sort of wanted to talk to/meet.

Thing is, usually people form groups and it’s rather intimidating to just randomly introduce yourself to a group. Even after 1 year there are many people I don’t know but want to talk to: boys and girls.

For boys: it’s a bit easier to talk to them as a boy myself, but how do I approach a dude sitting by himself, for example and talk? What to do I say to break the ice or how and where do I even approach him?

For a group: how do I introduce/join a group who are already engaging in a conversation, without interrupting them or something?

Girl: There are some girls I’d like to talk to (not romantically interested) and 1 who I sort of like-like. How do I approach them normally, as girls may be uncomfortable with a random person approaching them trying to talk.

Basically it feels weird to walk up to someone, extend your hand and introduce yourself. That would make me look like I am speaking to them for a specific reason or I am trying to sell them something lol

Thanks!