You can get to and from Balestrand by car, bus and boat. By boat, Norled has daily departures to and from Bergen to Balestrand and further into the fjord to Sogndal. Check timetables and prices here.
From the center of Balestrand to Dragsvik it is 10 kilometers and you can take the ferry to Vangsnes where you drive on to Feios/Fresvik or to Vik and over Vikafjellet mountain to Voss. Check schedules here. At Dragsvik ferry quay there is also a ferry crossing to Hella and Leikanger where you drive on to Sogndal. Check schedules here.
If you wish to explore the Sognefjord on your own, you can rent a car from Balholm Bilutleige.
Balestrand Fjord Angling offers Boat Taxi if you wish to take the trip to Fjærland. Contact Balestrand Fjord Angling for more information.