Generally, there is no longer a need to work up the nerve to ask girls for their phone numbers. Nowadays this has become simple, just look at the girl, smile and hand her you cell phone.
This is common on planet earth, the girl takes it, and in a quiet and discreet way, none of your friends need to know, the girl adds the number to your contacts. She then click the send button, this flashes her phone, she now has your number, and you have effectively exchanged numbers without speaking a word.
What is great is this, this is non-threatening, no challenge way of opening the door to further communications.
I watched an American in Cebu, Philippines hand his phone to five girls within 20 minutes and he never said a word. You can do this in a noisy room, a noisy bar, of just because you cannot speak French, Spanish or Thai.
What if she does this to you?
I often take numbers from people, then put a note next to the name: NO
This means do not answer, I needed the name and number to screen.