Find a theater, performance space or spacious room in which to hold your comedy show. Performing at a venue with a stage and lighting would be ideal, as it would allow you to capture the performer on film at an angle above the audience while well-lit. Contact local comedy clubs and community theaters about scheduling a performance date.
Set up multiple cameras so you can capture several different angles of the stage. Placing a camera at the wings of the stage, at the back of the theater and at a distance capable of getting a closeup shot of the performer would provide you with a wide variety of shots to edit together. Use a fourth camera to capture audience reactions of the performance.
Plug a recording device into the audio board that connects to the microphone the performer uses during the show, and place boom mikes around the room to record the audience's laughter. A direct feed to the sound board will give you the best audio quality to add to your film. Use a digital audio recorder plugged into the sound board to record the audio.
Assemble your film together using editing software such as iMovie or VideoPad. Feed your video and audio tracks into the editing software so you can use a time code to sync everything together. Keep in mind the pacing and flow of the performance when editing together different footage.