A plane is the fastest. But there is only one international airport in Estonia. So you have to know that you can only fly to Tallinn Airport and from there, you have to find a way to get further. By the way, Estonian Air offers really inexpensive tickets, if you book your flight well in advance.
From the airport to the Tallinn city centre you can take the minibus #15 that will meet every flight, price to the city centre is 20 EEK (~1,3 €). Bus #2 drives from 07:00 until midnight between the airport and the city centre every 20 minutes, price is 10 EEK (~0,65 €). Cost for a taxi from the airport to the Bus station: 60 EEK (~3,8 €).
Estonia has ferry connections to Finland (Helsinki about 20 times a day), Sweden (Stockholm and Kapellskär every second day) and Germany (Rostock twice a week) so you can also come by boat and then head to the Bus station or see below the instructions if you drive your own car. Cost for a taxi from the harbour to the Bus station is about 100 EEK (~6,5 €).
To take a bus from Tallinn to Pärnu, please see timetable. If you prefer the speed and convenience and money is not a question, you can also take a taxi from Tallinn to Pärnu. The fare must be pre-negotiated and should remain in the range of 1000 to 1500 EEK (65 to 95 €).
Taxi from Pärnu Bus Station to Pärnu Airport, where is the dropzone, or to Jõekääru Kämping (the official Parasummer camp) takes ca 15-25 minutes and 70-90 EEK (~4,5-5,8 €).
By car you have to prove that you are a geographer and you can find the place by yourself :). If you are approaching from Latvia then use Ikla/Ainaži or Valga/Valka border for getting into Estonia. Via Michelin and Map24 can help you in becoming a geographer :)
If you are driving from Tallinn to Pärnu by car take the road E67. Continue along E67 for 130 km. When arriving to Sauga crossroad (a few kms before Pärnu) turn right and drive 4km until you see the sign “PARASUMMER CAMP”.
Pärnu Airport -- you can understand that you are in right place when you see the sign “PARASUMMER DROPZONE” on the gate.
It's not that hard and so we hope to see you all very soon!