Do you have a powered mixer?
Do you have powered (active) speakers?
If you don't have a powered mixer or powered monitors, you need to get a power amp. You would then plug the main outputs of the mixer into the power amp and plug the speakers into the power amp.
It sounds like you're talking about regular passive speakers, so you need a power amp of some sort (in consumer grade home stereos they're often just refered to as 'receivers'). Then you plug your soundcard output into the power amp similar to hooking up a cd player to the receiver.
If you don't have anything you can use for a power amp, you may want to invest in a pair of powered monitors rather than buying a power amp to use with low-end (I'm guessing?) bookshelf speakers.
Good luck
Use the control room outputs on the back. You can adjust the volume with the control room volume knob that way. (it's the same control for the headphones)