Buy a RCA (what you have on your mixer) -> jack cable (like your walkman/mp3 player headphones) on ebay.
Stick the jack end into the line in of your soundcard. If you don't have one, then buy yourself a new soundcard, they're extremely cheap.
Open Audio Recorder in Windows or the recording program that came with your sound card. Set up the volumes in your Windows control panel so that you are recording input from line in (generally you can only record from one external source).
Press record. Start mixing. Stop mixing. Press stop. Convert to 192 or 256 mp3 and upload.