Use the console commands recorddemo demo_name,  playdemo  demo_name and playdemo stop. Example:

recorddemo uc_vs_uc // starts demo recording
stoprecording // stops demo recording

playdemo uc_vs_uc // starts demo playing
playdemo stop // stops demo playing 

You can also save hard disk space by setting com_compressDemos to 1 before you record. The only downside being a slightly longer pause before playback

It should be noted that demos are recorded at a maximum of 30HZ.

See the FAQ How do I access the console? for details on how to enable the console.