I was at the supermarket some days ago and I wanted to pay part in cash and part by my bank card. When I asked this girl wether that was possible she said no, but it is. I was just being polite, like letting her know in what way I want to pay.

Should I have responded 'I'm sure you'd like to make an exception for me'? Does that sound well?

Yes.

Alright, I'm on the right track to becoming a master pick-up artist then! Thanks.

Had another supermarket scenario, this is going to be incredibly hard to translate from dutch to english though.

Me buying some bacardi and I just say hi to this girl and look at her in the eyes for a while, then pay. She asks wether I want the... ehm I think it's called receipt? Not sure.

Anyway I say 'No thanks I don't do those' (now this may sound a bit weird in english, but in dutch it always makes the girls laugh who are working)

She laughs, I smile. I say now you won't have to print out that receipt. She: 'Yeah we're environment friendly'.

Me: 'Seems like I made your day'. She then laughs and we say goodbye.

Did I do alright? This is really frustrating because I can't translate it well, it all sounds so different in dutch.

Yes, it's a receipt. Good translation, I think.

If you got her to laugh (as long as she didn't laugh AT you), you succeeded. You could have gotten her number at that point.

For real? I could have just asked 'Hey, can I have your number?' it seems a bit soon... but I might try next time. I'm obviously new to this.

Girls give out their number all the time. It's nothing that really even needs to be earned anymore. You made her laugh, and that's pretty much all you can do given the circumstances. Instead of asking for her number outright, word it like "You know, I think you're adorable. Let's get some drinks on Friday. Give me your number." Alter the wording to suit your personality, of course. There's no guarantee it'll work every time, but what do you have to lose?

That's true man, I think she was about 2 years older than me though. I'm 19. But no problem! Next time I'll go for it.

Would this work also? Tell her to print the receipt out anyway, hand her a pen and then say "show me how creative you can be"

I think I've seen something like that on mystery's show.