Instructions
Start Steam from the desktop icon or start menu. The program will boot to a login screen.
Check the "Remember by password" box and log into your account.
Launch "Garry's Mod" to see if there are any updates available. Once the game boots up, you may immediately close it.
Click on "Setting" from the "Steam" menu on the top toolbar.
Un-check the "Don't save account credentials on this computer" box, if necessary. By default, this is already turned off.
Open the Steam menu and click "Go Offline."
Click "Restart in Offline Mode," and you now have the ability to play "Garry's Mod" offline.