How do I wire in a bathroom light/fan to this box?
This write-up assumes supply power is coming in from the bottom cable. It's a little hard to tell what the blacks are doing. 

Typically when electricians install light/fan wiring, they use /3 cable so that black and red can be used to separately control 2 things. (white white as neutral return). 

Why they ran a /3 cable to your vanity, I really do not know.  I have a feeling this /3 cable goes up to your ceiling box, then a /2 comes down to the vanity.  In that case, one wire (e.g. Black) feeds the vanity and the red is capped off waiting for use with a ceiling fan. 

In your case, it was wired without separate control, as the red and black are connected to the same screw of the switch, using an illegal double-tap.  You are about to correct that.  

Split it: the supply cable (from the GFCI) goes to a black "common" terminal on the dual switch, and then each of the red and black wires go to separate brass terminals.  That will give you separate control of red and black.  

Up top, you'd need to connect red and black separately to different devices.  Both use white for neutral. 

Don't pull the splitter in the back of the switch, and don't take the tape off the terminals.