Pick a scoring system for your game. Most recreational games award one point for normal shots and two points for shots made beyond the three-point line. Feel free to use conventional two- and three-point scoring if you prefer.
Set a winning score. One-on-one hoop games usually end at 11 points. Also common are 7-, 15- and 21-point games. Set a high winning score if you're using conventional scoring.
Next decide on possession. Winner's outs (or 'make it and take it') gives you the ball back after you score. Loser's outs gives the ball to your opponent after you score.
Determine a clearing point: a spot where each player must take the ball after rebounding an opponent's missed shot. This establishes continuity by giving both players a chance to set up for the next play. The three-point line is almost always used as a clearing point.
Start the game once you've finished arguing over who gets the ball first (or be quiet and shoot a free throw to decide).
Call your own fouls as they occur. Agree on whether you want just defense to call fouls, or just offense (or anyone at all). Decide between shooting free throws and awarding possession to the player who has been fouled. Once it's decided, stick to the choice.
Run the ball back to the clearing point. Rematches give the losing player a chance at redemption, while providing the winner with opportunities for further gloating.