Installing an exhaust fan in place of a light fixture
The choice is yours to make based on how much control you want.

Do you need to control the lights separately from the fan?

(do you mind if the fan comes on every time the lights come on?)

If no:

Just wire all the black wires to your existing black wire, the whites to white, and the ground to green and you are done!

If yes:

You'll need to run another wire.

If you decide you need to run another wire you need to ask your self

Do you need to control the lights independently from one another?

If yes:

Then you'll need to run 14/4 wire and 2 more switches. (instructions below)

If no: 

Then you can use the 14/3 you bought, but will need an extra switch.

Instruction for connecting new wire:


Connect all neutrals in the fan/light box together with the neutral (white) of you newly run wire. 
Connect the neutral wire directly to the neutral (white) in your switch box
Connect the green grounding wire to your copper or green wire of your newly run wire.
Connect the green (or copper) grounding wire of your new wire to the grounding wire in your switch box with an added jumper if required for your switch.
Connect each of your switches to your the hot wire in your switch box via jumper wires
Connect each switch then distributes power to one of the remaining colored wires  (and take note of the order)
Connect the other end of the wire to the desired device you want it to control