Look at the back of your CD burner. Identify what kind of input cable you need to run from your sound mixer. Usually you will be using RCA cables. Your sound mixer should also have RCA outputs on the back of it.
Plug the RCA cables into the stereo output on your sound mixer and into the stereo input on your CD burner.
Plug in your two sources of sound into the sound mixer in two tracks' input jacks in the back of the sound mixer. Plug your headphones into the headphone jack on your sound mixer.
Have the two sources of sound play or speak or sing. Listen to it through the headphones. Make sure your master fader is turned up. Raise the volume of your sound sources with the faders on the sound board. You can also adjust the gain, which is a knob usually at the top of each track on the sound mixer. Tweak the sound with the equalization knobs if desired. What you hear in the headphones will be what is recorded on the CD burner.
Put a CD in the CD burner. Hit "Record." Tell the two sources of sound to begin. The CD burner will record everything in real time.
Hit "Stop" on the CD burner once the performance is over. The CD burner will ask you if you want to finalize the recording. Once you do this, the recording is permanent on the CD.
Play the CD to make sure everything recorded as you wanted it to.