I hope you understand that there are so many wiring combinations and way electricians run wires that I can't give a basic wiring diagram for fear of someone electricuting themselves which is why I need to identify all wires. The hot wires from the breaker could be going into the switch box or the fan, there could be hot wires continuing on to another location such as a light or receptacle, or you could have other 3 way or 4 way switches on the walls all interconnected.
Start with the switch box. If you only have a black, white, and ground inside of 1 sheathed electrical cable sheathing with the black on one side of the switch and the white on the other, then you probably have a switch leg. In a switch leg, the white wire is hot and should be identified by having black tape or black paint on the white. The black mark should also be on the same wire in the ceiling. However, if you have a switch leg, then as the other poster suggested, you will need to run 3 wires(red, black, and white) with the equipment grounding wire as the 4th to put in 2 separate switches as well as changing the box to a double gang. If this is what you have then there is no need to remove the ceiling fan until you determine if you can run new nm-b sheathed electrical cable through the wall and attic. Let me know if you have conduit instead of sheathed electrical cable.