To watch a demo-record file, first you must get the file from the server owner, or someone who could provide that demo. If you're ingame and see DemoRecSpectator on the bottom of the player list, that means a demo is currently being recorded.
I know that Both CT and FPI record every match -- I can not speak for any other server. If you do not see the DemoRecSpectator on the player list, you need to open your console ("~" or F5) and type "DemoRecord", or ask an admin to start an AdminDe