Suburban Gothenburg consists of the municipalities just east of Gothenburg in south-western Sweden.
Public transport in the area is organized by Västtrafik. All listed municipalities have local trains going from Gothenburg. Mölndal is larger, and tram or bus connections from Gothenburg can be preferred for many destinations. Search the Västtrafik site for connections.
From the Landvetter and Gothenburg City airports, the airport bus to Gothenburg (going directly from the airport building) and then train is preferred.
Tickets for Västtrafik can be bought by credit card onboard, but not for buses in Gothenburg. Pressbyrån (e.g. at Landvetter airport) and some other shops sell tickets (not at City Airport). The airport bus need special tickets which are bought with credit card onboard. Read the Gothenburg entry for more ticket details.
Inside the municipalities there are buses. Inside Lerum, local trains might be preferred. All are organized by Västtrafik. The city and village centres are small so walking might be a good option. Mölndal is a little larger.