Click on the links below to find out how you can get from Tromsø airport to; 

Lyngseidet
Nord-Lenangen
Furuflaten
Koppangen

Try out the trip  - planner on; http://www.177troms.no/

Bus schedules from Tromsø to Lyngen here;
http://www.vitaminw.no/kunde/cominor/Filvedlegg/150_09.pdf.pdf
http://www.vitaminw.no/kunde/cominor/Filvedlegg/150-155.pdf
http://www.vitaminw.no/kunde/cominor/Filvedlegg/460-462.pdf

The nearest airport is Langnes Airport, Tromsø.From Tromsø you can drive through Breivikeidet (Get off at Fagernes - Route 91) with a ferry over Ullsfjorden:

Ferry schedules here...

There is a speed boat going from Tromsø to Nord - Lenangen 4 daus a week.
Boat schedules here... (PDF)