Step 1:
Open Windows 8 Skype app

Step 2:
go to Charms Bar (Keyboard shortcut: Win Key + c)

Windows8CharmsBar

Step 3:
Then go to settings charm

Step 4:
Select options

windows8Skype

 

Step 5:
You can see the sign out from the windows account linked to Skype.

Windows 8 Skype App