"Flughafen Bern" is a small airport near the capital Bern. Most flights originate from Europe. Intercontinental flights arrive at Zurich airport.
Free transportation from the airport to Bern
There is no train station at the airport. A 10-minute bus ride takes you from the bus stop "Bern Flughafen" at the airport to the rail station of Belp, from where you can continue by train to Bern or Thun. Also, there's a bus to the rail stations of Rubigen and Münsingen.
The Swiss Travel Pass and several other rail passes cover the buses for free, as well as the trains. If don't have a Swiss Travel Pass, the trip from the airport to Bern via Belp is also free if you have booked a hotel or other accommodation in Bern, since they will issue you a Bern Ticket.
There are rental cars available at the airport too.