A friend of mine got Skyrim, we installed Steam and the game on to his computer from my house since he does not have internet at his house. Yet every time he goes to play the game it trys to log into Steam. Do you have to have internet to play Skyrim on the PC?

You need to manually set Steam to Offline mode after installing -- Also once you have the game settings setup instead of using the SkyrimLauncher.exe file to launch the game try using the TesV.exe file to launch instead (It is in the same folder) - this is the actual game launcher and I have heard it will launch the game without launching Steam (only problem is this method will not let you change settings from the launcher so you will need to use the SkyrimLauncher.exe any time you want to make setting changes (other than those in the In Game menus) or any time there are patches needed (but any other time you can launch the game by using the TESV.exe file and avoid loading Steam.)

Although, if you want to earn achievements while playing, you will need Steam to be online.

You should have read the games requirements. You have to have an internet connection to activate the game through Steam.

Edit:
Misread the post, if you activated it at your house then all you need to do is set steam to offline mode.