As the only direct flights to Pärnu Airport are from the tiny islands of Kihnu and Ruhnu, it's doubtful that you'll be coming straight in by air rather than transferring through Tallinn or Riga (explore bus connections from those airports). That said, it's theoretically possible to charter a plane from Tallinn. Pärnu's airport, originally part of a military airbase, is headquartered in a compact and modern building, and has only minimal services.
Getting to town Bus N°23 makes the 7km connection to the city centre, but leaves only twice per day. See 'Taxis' later in this section for numbers.