RDR1's duel system is super easy once you learn how it actually works.
How Duel Works
The Red Bar is for your opponent and the Blue Bar is your bar. What you need to do is fill your bar faster than your enemy does by pressing shoot button repeatedly at the aimed location.
Disarm: Aim at your opponent's hand and wait for the aim to turn white and get small, then press shoot button repeatedly.
Kill: Aim at your opponent's chest or head and wait for the aim to turn white and get small, then press shoot button repeatedly.
How to find people for Duel
Drunk Stranger: Sometimes random drunk strangers will challenge you to a duel. This strangers have a Blue Dot marked in your mini-map.
Cheat in Poker: If you cheat in Poker while wearing Elegant Suit, and get caught, one of the npcs in the table will challenge you to a duel.
1. Buy the Elegant Suit from a Tailor for $70 in any city.
2. Start a Poker game.
3. Choose cheat option using the designated button. (Y/Triangle)
*. Start the Poker game and immediately choose "Skip to your turn" option to see the Cheat option.