Note that the Airport and Central Dresden are within the Dresden tariff zone; a single ticket is valid on the S-Bahn, trams and buses within that zone. Other tariff zones cover the surrounding towns as far as Meissen and the Czech border.
The Dresden Airport railway station is right in the basement of the passenger terminal and serves:
Line S2 of the Dresden S-Bahn, running every a half-hour to Dresden Neusadt, & the main train station ('Hauptbahnhof') in Dresden; the trips take 12 & 20 mins each. Weekdays the trains continue to the towns of Heidenau and Pirna.
DVB bus route 80 offers connection from the Airport to Elbe Park shopping center & on to Omesewitz, and at opposite directs to Grenzsrasse railway staton (interchange to S2), K.Kolwitz-place (interchange to tram line 7, and Dresden-Klotzsche railway station (interchange to S2 & regional services).