When I meet someone new, I introduce myself and they do also, but then it gets to the part where what do you say next? I know it's pretty basic, but not for meeting girls for instance, just a general talking to anyone thing. like for example

Hey Im John Doe...

Hey John, I'm Tim nice to meet you.

Then what do I say?

I never introduce myself, wait for them to ask.

As for conversation there are a few things which will help you out loads, the first thing is have your first two conversations planned, this would be your opener then the thing you stack on top of that.

Then I find a little dipping into what they do (especially effective in school game) works wonders, form this you can talk about ambitions (hers/yours) then ask what she wanted to do as a kid.

Essentially you want to be stacking related topics but hunt for hints at things she says or implies and investigate them. For example a girl recently told me;
HB: I work in a crappy restaurant
ME: what do you want to do
HB: I don't know
Me: Ok if you could be anything in the world what would you be?
HB: A dancer
Me: thats cool I love dancers. Ooh what's your favorite musical?
etc etc

you just need to be chatting, if something crosses your mind say it get their opinion, make fun of their choice in music , just act like she is a friend you have known for years. Hope this helps

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