How Do I Connect The Wires To A Ceiling Fan, The Junction Box Has Black, White And Copper, But The Fan Has A Blue Wire, Which Do I Connect It To - Black Or White?

There is more than a blue wire. There should be a white wire and a black wire and a bare ground or green wire. Usually the blue wire is for the light kits on the fans. It is usually pulled through the fan to where the light kit is attached that is what powers your light.

There should be a blue a black a white and a ground coming out of the fan,if there is then wire nut the blue and the black from the fan to the black in the junction box,blue is usually the color for lighting,black will bring power to the fan.Now if its a newer model that comes with the lighting kit and there is only blue white and green then go blue to black,white is usually always neutral (unless its a cold switch or a dead end switch leg)white usually goes with white.

Does not matter power or ground (you have already killed the power at the breaker) green is ground goes to the copper wire in an older house no need for green just tuck it inside, blue goes to black (or red) usually for the remote and of course white to white.