Before you can use any of these cheats, you have to enable cheats in the console. Run Half-Life with the -console switch to enable the console if you don't have it already.
To enable cheats, the server variable "sv_cheats" has to be set to 1. The change won't take effect until a level change has taken place, so:
1) Type "sv_cheats 1" (minus quotes) in the console. If the game is multiplayer, you must be running the server to do this or use rcon.
2) In a single player game, either press F6 to save the game and then F7 to load the game or go through a level change. In a multiplayer game, use the changelevel command to change level or wait for a level change to happen as normal.
Once sv_cheats is enabled, you'll be able to use all the cheats listed above.