Brinith:
I was wondering if I could use the Arduino Uno's PWM pin to control a PWM fan's speed
Nope. Whoops, sorry, [backspace] [backspace] [backspace] [backspace] [backspace] [backspace] Yep for sure. The only caveat is that down at -low- RPMs DC motors often get boggy.
and supply auxillary power to actually drive the fan.
Pretty much nope. Arduino can supply only a tiny amount of current.
I will be using it as a control hub for the rest of my computer such as fan speed, lighting, temperature, etc.
If its possible, then how would I go about doing so?
Google is your NEW best friend. 
Look up...
site:arduino.cc "computer" "fans" "fet" "12v" "pwm"
...-including- all the "quotes" and your friend will return a bunch of very relevant hits. Start reading and come back again when you have a Q.
Also the 12V supplied by a molex plug in a computer's PSU would be enough to power the Arduino right?
Yep, plenty, that's exactly what they're for. You don't -have- to buy Molex connectors you can cut/splice/extend them manually.