How do you install a ceiling fan with red black and white wires?

Based on your description it is very likely that either the red wire or black wire is switched and the other is on all the time. In most cases the light of the fan, if it has a light, is connected to the switched wire and the fan is connected to the unswitched wire. This allows you to turn off the light while allowing the fan to remain running. There is no way to know without testing which wire is switched.

The white wire is the neutral, connected to the white, or neutral, or common conductor of the fixture. There should also be a bare or green wire in the box to connect to the ground wire of the fixture.