Logged in for the second time, I am clicking on teleport, it says Second Life is already running.

[MissEuqinom]

No idea where to find my Avatar, I only see a screen with my account information. First time I logged in I was at Learning Island. Logged out yesterday en trying to play again today. Can not.

[Syo Emerald]

That message would mean, that you are trying to open another instance of your viewer and try to log in from it, while already being logged in. (And refering to your headline, you can not teleport, when you are not logged in, so this does not make much sense).

So the question is: Have you opened the viewer, typed in your account name and passwort and then clicked to log into Second Life?