I am a big fan of the exhaust fan timers. Sometime you want to let the thing run for a while after.....well...after you are done. The ones I use have the 5,10,15,20 minute settings.
Take apart the jbox on the fan and see what you have in there. They are generally really small so there may be another jbox in the mix.
Post the results and we can guide you through it.
IF the 120V hot power is in the fan jbox, simply replace the two wire cable leading to the switch with a 3 wire cable.
In the fan Jbox, wire the black to black, whites to whites, and red to the ex fan (the black lead going to the receptacle)
TURN OFF THE POWER. The fan MAY have energized conductors in it even though the switch is off.