To be sure, we also use name cards in North America but not as often or in such formal spirit. When you meet somebody for the first time, be prepared for the exchange of cards. Wait for the other person to give you the card first. Unless you are sure that he or she considers you higher in social rank and does not feel at liberty to hand you a card first, then you can hand out your card and ask for one. Yes, pretend if you have to, but be sure you do all this with due respect.
Respect here means a couple of different things.
First, when the gentleman or the lady hands you the card, remember to receive and hold it with both hands. And with both hands you give out your card. Once you have the card, you are expected to study it somberly if not admiringly, still with both hands. Be sure to spend at least 7 seconds studying the card. If you like, you could mumble something unintelligible.