Its ok, everyone is here to learn....
If you want to record things at the same time but onto separate channels, so that in your software you have a separate track for bass, drums, vocals, etc. then you need an interface with enough inputs to handle it. This interface will replace your stock soundcard, you bypass that totally.
In fact, other than using it's pre-amps, if you're working this way you don't need a mixer at all, you just go straigt into your interface and record directly and mix in your software.
Now, if you simply want to connect several instruments to your mixer, adjust the levels the way you like and record that mix onto your computer, then all you need to do is connect the master outputs (stereo) to your soundcard. What cable you need depends on the jacks of your equipment. Of course, this way what you record is what you get - you can't re-mix it later.
However even if this is what you want to do, to simply record a stero master that you've mixed live off the floor, I would recomend upgrading your soundcard to one designed for music production, like the Audiphile 2496 as an example.
Hope this helps!