Powering Uno and some LED's from a PC PSU

Hello! I have just bought my arduino uno, and i am trying to do some silly stuff with it.
First of all, i know that the question of using a PC PSU has been answered a lot of times, but i didnt find anything about LED's.
So i got some common cathode RGB LED's and as i understand i cant power them all from the arduino, because it cant output enough current. So i need a power supply, but i dont have one.
Can i wire them up on my PC's PSU through a molex or sata connector?
So ground goes to a molex, and the other pins go to the arduino.
Is this going to work?
I am sorry, i am quite new to electronics and the arduino commnut.

Some rgb leds can be powered by the Uno. Post a link to the spec of your leds. How many leds? Do you need individual control of each led?

Hello! They are some cheap-o LED's that i got from ebay. Nothing special.
This is what the seller posted bellow them on the sell page: http://tinyurl.com/lnabbr8
For now, i dont have a plan, so i dont know how many. The max number would be 12(because thats how many led's i have). But in that case i need a led controller chip, right?
Would be nice if i could controll all of them, but once again, i think i need a led controller, right?

Thanks for the reply and thanks for the help!

Each led could draw up to 60mA. If powered by usb the Max current is 500mA, of which at least 50mA is taken by the Uno. So you can power perhaps 7 of them. With reduced brightness, you could power 12 on USB power.

However, the atmega328 chip has an overall limit of 200mA and individual pin limits of 40mA, although it's wise to stay well away from those limits.

So it all depends on how bright you want them and whether you want individual colour control of each led. You can control all 12 individually with just a few transistors and USB power, but the brightness would not be the maximum the leds are capable of, but perhaps still bright enough.

The Uno has 6 pwm outputs, so you could arrange you 12 leds, electrically speaking, as a 6x2 matrix and use a 1:6 multiplex.