Gather all the CDs, vinyl, or MP3s that have the songs you want to go into your mix.
Use a multi-track audio program (e.g. Acoustica, Ableton Live, Audacity, Cubase, etc.), import the songs into an audio channel in the order you want them to playback.
Stack each song and file back to back so that they flow into each other.
Once you have all your songs in place, under the file menu choose "Export" and export the entire mix into one audio file (WAV, AIFF, MP3, etc.).
If your audio program does not export to MP3, find the WAV or AIFF file and convert it into an MP3 using iTunes or any other MP3 encoding music player.
If you are performing music with multiple software programs you can route them through an external mixer for more refined control. Open the software programs you will be using to mix music.
Assign each program's main audio output to a stereo pair on your audio input/output interface.
Using 1/4" TRS or RCA cables, connect the corresponding outputs from the interface to the input channels of an external audio mixing console (Mackie, Allen & Heath, etc.).
If you have a digital mixing console and a digital-enabled I/O interface for your computer, you can route all the channels through a single Lightpipe cable (SPDIF, Optical).
Trigger the music or sounds from each program to play in the transport section.
On the mixing console, turn up the individual channels assigned to each program until you achieve the sound you want for your mix.
This output mix can then be recorded to an external source such as a rack CD recorder, MiniDisc recorder, or a secondary computer running an audio-editing suite such as Ableton Live or Digidesign Pro Tools.