The quickest way to get this started is call up a friend and ask to play some pool. This can be done while you're working for any of the friend achievements, such as "Dial B for Bomb" and also when you're trying to pick up a girl for "Warm Coffee."
After you pick your friend up, the location will be on your radar. Once at the pub, walk up to the table and start the game with . Billiards can be a rather complex game, but GTA has done a fairly good job of simplifying it. In essence, one player shoots the striped balls in, the other shoots the solids, and once a player has their balls sunk, they may shoot for the 8-ball. When the 8 is pocketed after all other balls are, that player wins. However, if the 8 is pocketed before the rest of your balls, you lose.
When it's your turn, you will see a dotted white line coming from your ball. This is the path your ball will take when you shoot. The computer actually does a very good job of lining the shots up for you. If you do no aiming, take the shot that it gives you, you should make the ball almost every time.
When you are looking down the path your ball will take, press to enter shooting mode. Now pull back to pull the stick back, and push it forward to shoot. Those are the basics you will need to win the game. Almost all advanced billiards mechanics such as English are included in the game, but to obtain the achievement you shouldn't need to worry about those things.
If you find yourself struggling, as is stated, one of the main rules of billiards is if you shoot the 8 ball early, you lose, so wait and eventually an opponent may shoot that ball in for you, granting you an automatic win.
**Can be done after completing story mode**