In which countries is the expression to hit on somebody (to flirt with) common? In everyday English, what's the most common way to convey the idea?
"hit on" is slang and may be considered crude.
"approach" is another word that can be used.
I'd like to approach that girl and get her name.
I'd like to meet that girl . . .
I'd like to introduce myslef to that girl . . .
To echo Susie, to "hit on" someone is predatory. The person hitting on another is generally trying to get sex.
Firting is fun and light. You can have innocent flirting that isn't intended to go anywhere except to create some smiles. Maybe it will lead to more, but it's not necessary.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
I am not a teacher.
We can also schmooze a girl stateside.