The program Audacity is a fully-functional, multi-track recording environment meant to record everything from line-in to your stand-alone mic on the computer. Audacity is also capable of recording your PC audio, or whatever sound is coming out of your computer's speakers.
Download and install Audacity for free at audacity.sourceforge.net. Once installed, select either "Stereo Mix" or "Wave Out" from the drop-down menu in the top right of the application. Locate the PC audio sound you want to record and press "Record." Hit play on the sound you located and watch the meters to make sure it's recording. Stop the recording after the sound you want is done playing.
From the File menu, choose "Export" and you'll be able to name and tag each file you record. Once done tagging, you have the option of saving the file in different audio formats, like WAV, MP3, OGG, FLAC, M4U and AIFF among others. You can do this as many times as you want and as long as there's sound coming from your speakers, you can record and save it in Audacity. Plus you can make an audio CD to play anywhere or transfer the new files to an MP3 player.
Besides Audacity, other free recording software programs are Pro Tools Free, KRISTAL, Quartz Audio Master, FreeCorder and Anvil Studio, among others. They all come with instructions and user guides to help you navigate the software.