Dueling is easy. When it says "Draw" you pull back on the right analog stick, then push it forward as quickly as possible to draw your gun. You then use the right bumper (I think, I didn't play it on 360) or R1 to mark your target as many times as you have bullets in your gun. Headshots are preferable, but if you would rather go the path of nonviolence you can also aim for your opponent's gun to shoot it out of their hand, or their hat to scare them away. The crosshairs will change size from large to small, and when they're small is when they will be most accurate.
Anyway, that's how you duel. Enjoy it. Also, if you have the elegant suit you can cheat at poker. If you want to practice dueling you can simply go to a cheap poker table and get caught cheating. It'll trigger a duel sequence and voila, instant duel practice!