For this trophy, you need to play 10 games of Blackjack. This can only be done in casinos. There are 5 casino's in the game (6 with the Dead Money DLC):
Atomic Wrangler (Freeside)
Vikki and Vance Casino (Primm)
Gomorrah (The Strip)
The Tops (The Strip)
Ultra-Luxe (The Strip)
Sierra Madre Casino (Sierra Madre) *The DLC casino*
First you need to purchase chips, which are the currency in the casinos. You can pay for these chips with either caps, NCR Money, or Legion money. Each casino has its own chip, so you can't buy chips in one casino and have them count in another one. After you bought chips, head on the one of the Blackjack tables inside the casino and start playing.
It's not neccesary to know the rules of the game, since you don't need to win. Simply playing 10 games should make this trophy pop up.
Hope this clears some things up.