Plug an XLR or 1/4-inch cable into the output on the receiver of your wireless microphone. Usually wireless microphones use XLR cables, but some use 1/4-inch. Plug the other end, the male end, into a track's input on your sound mixer.
Plug RCA cables into the master output on your sound mixer. Plug the other end of the RCA cables into the input on your CD recorder.
Test the sound and adjust levels. Set your master fader and the fader of the track you are using to zero. Turn the gain knob on your track to add signal to the track. The gain knob is located at the top of the track. Listen to your sound through headphones. Once you have achieved the sound you want, you are ready to record.
Put a blank CD into the CD recorder.
Press "Record" on the CD recorder. Tell your wireless microphone sound source to begin performing.
Press "Stop" on the CD recorder once the performance is over. The CD recorder will ask you if you want to finalize the CD. If you like how the performance went, agree to finalize the CD. Once you have finalized, you will not be able to record on the CD again. You can now listen to the recording on CD.