The roulette wheel operates by spinning in one direction while a ball is spun in the opposite direction around the edge. The wheel is divided into numbered pockets, alternating in red and black, with a single or double green zero depending on the version. Players place bets on where they think the ball will land, choosing from various options like specific numbers, colors, or ranges. Once the ball slows down, it falls into one of the pockets, and winnings are paid out based on the odds of the chosen bet.