Question: There is an existing light fixture and switch for the light fixture. I want to add a bath fan with its own switch. 

What is the easiest way?

Answer: 
If you're not comfortable working with electricity then hire a professional. Improper wiring and the resulting fire isn't worth saving a few bucks.

That said:

Your existing fan/light combo is likely connected using a 2-conductor cable (like 14-2)... but for two separately switched circuits you'll need three conductors (14-3) or two separate 14-2 wires.

At the gang box, one of the conductors goes to the light, and the other goes to the fan.
You need to check to see how many wires you have going into your current switch from the fan. It is most likely that you have a black and a white. 

If this is the case you will need to run either 12-3 or 14-3 wiring from fan to switch. Size dependent on amperage of circuit. 15A gets 14 and 20A gets 12-3. 12-3 will actually work for either. You need to hook up the wiring for the fan part of the kit to the extra cable (red) and to power. The other side of the red powers your individual fan switch. 

The hardest part of doing this is getting the cable from the fan to the box inside the wall. This usually consists of taking out and patching drywall. Not counting the drywall issues, this is a 30 min job.

Now if you have a white, black, and red (or two blacks) currently coming into your box then you are in luck. You simply need to install a bigger box where your current one is and take the fan power (red or extra black) to its own switch.