To request chip colors at a casino table, approach the dealer and politely let them know which colors you would like. You can mention the specific denominations you need, as different colors typically represent different values. It's helpful to do this during a natural pause in the game, ensuring you have the dealer's attention. If you're unsure about the available chip colors or their values, feel free to ask the dealer for guidance. Always remember to communicate clearly and courteously to facilitate your request.