There are at least 2 ways to do that:
1. Use Half-Life's built in demo recorder.
2. Download Fraps.
To use HL's demo recorder, open the console while playing in game. Type "record blah" with blah being the name of the file. Then, when you're done recording, open the console again and type "Stop", and the demo will stop recording. Oh, and don't use quotations, except for the file name. Example:
Record "Blah blah blah". Blah blah blah will be the name of the file, and will be located in your mod folder, with the name "Blah blah blah.dem".
If you don't want your video to be in DEMO format, then you must download a program called Fraps at
http://www.fraps.com
Hope this helped.