We were surprised in our ignorance at not having to present our passports. Silly us-Poland has been a member of the EU since 2004.
After climbing down the portable stairs and riding an airport bus for about two minutes, we walked through a small and decrepit Terminal 2 arrivals area and emerged into the sunshine.
From there, it's a 10-minute walk all the way around to Terminal 1 and the shiny new Hilton Garden Inn (there's a shuttle between teminals that would be handy in poor weather, but we enjoyed the walk).
Here we are - nice place!