You'll obviously need a cable with the relevant terminations. If this is the case, you can simply plug the outputs of the mixer (in this case either the Stereo Out, Monitor, Rec Out or Aux Send) into the input of your on–board soundcard.
It's likely that your computer has an 'on–board' soundcard, and yours may have line and/or microphone inputs on mini-jack connections. News Editor Chris Mayes–Wright replies: To get the audio from a mixer (or any source) directly into a computer, you'll need some kind of audio interface - also known as a soundcard. The output section of a mixer may have a number of different connectors (this Yamaha MG102 only uses jack sockets), so you'll need to have the correct cable to interface with the PC input. Referring to your article in Q&A from SOS January 2007, regarding a basic home recording setup, can you connect the Yamaha MG102C, which you suggest, to a PC directly? If so, how?