Half-Life does not require an internet connection.
If you're running the game from Steam:
When you fire up Steam, it will try to log in your username at the server. If it doesn't detect an internet connection, it will give you an error message. There you will have an option saying 'start in offline mode'. Click on that, then run the game.
If you purchased the disc from a retailer and don't have a Steam account:
You'll need to create an account on Steam. After that, run the game from Steam like explained above. Yes, if you're creating a new account on Steam, you'll need to have an internet connection. However, once your Steam is downloaded/ installed, you won't need the internet to run the game.