Salzburg is easily reachable via Salzburg Airport, and Munich or Vienna Airports.
Salzburg Airport offers flight connections from many European destinations.
The city has also a good accessibility by train. Travelling time from both the Munich and Vienna airports are approx. 2 1/2 hours.
Useful links:
Austrian National Railroad http://www.oebb.at/en/
Germany National Railroad https://www.bahn.de/p_en/view/index.shtml