Hi mate, I don't know the mixer off-hand, but in general they have two outputs, one for master volume and one for booth volume. I have master going to my PC which I never alter (so it always records at the same level) and then locally in my room I just use booth, which goes to the amp, speakers etc.
What you need to do is simply put your output to your PC. You'll need the lead that starts as a red/white audio cable at the mixer, going into a headphone jack fitting at your soundcard end.
The thing to watch for without an amp is that if you turn it up on the mixer so you can hear it louder in your room, you will, in the process, turn up your record volume, which will spoil the recording.
So always keep master on the mixer the same and if you want it louder for you, adjust the speakers, not the mixer