There is an hourly (almost) bus (RVO 840, the Watzmann Express) from in front of the Salzburg Hbf to the Berchtesgaden Hbf. From the Berchtesgaden Hbf you take RVO bus 838 to the Dokumentation Center/Kehlstein Busabfahrt. If you buy RVO Tagestickets at €9,- per adult from the bus driver in Salzburg, it will cover your round trip Salzburg-Berchtesgaden Hbf-Kehlstein Busabfahrt, indeed, all travel on RVO buses for the day. The special mountain buses up to Kehlsteinhaus (The Eagles' Nest) and back will be extra. You buy tickets for them at the kiosk at the bottom of the mountain below Kehlsteinhaus (at the Kehlstein Bus Abfahrt). The ticket includes the elevator to the Eagles' Nest from the bus parking area below it.
Be sure to tour the Dokumentation center also, with remains of the SS bunkers in the area.
I've done the Eagle's Nest twice on my own, but always from Berchtesgaden, not Salzburg.
There are many Salt mines in the area around Salzburg. One of them is in Berchtesgaden. It looks like it is "Salzbergwerk", two stops beyond the Kahlstein Bus Abfahrt stop on the bus 838 route.