I've been happily using SKYPE for a long time on my Lumia 820, but since the recent SKYPE update and the need to link a Microsoft account, I cannot access my existing Skype account (which has all of my contacts).
For some reason it didn't link my existing Skype account when signing in for the first time, and now I have an empty Skype account (for my Microsoft account) and I can't see anyway to sign out anywhere in the settings.
I've deleted the app and reinstalled, but it gives me no option to link a Skype account.
You will need to unlink your Microsoft account from the empty Skype account first, then the next time you login you will be prompted to link your correct account. Here are instructions for unlinking:
Hope this helps!