Gili Air is relatively easy to reach no matter from which part of the world you come. You can reach the island by plane and boat to gili.
Flights to gili air
The Gili islands are part of the West Nusa Tenggara province, so you can find flight to mainland Lombok that has a new International airport Praya in Mataram, the capital of Lombok. To reach the airport, there are some international flights that are scheduled daily from Jakarta, Bali, Singapore and Malaysia.
Once you arrive in Mataram, just find taxi and ask them to drive you to Bangsal port. From Bangsal you take the boat to Gili Air.
Fast boat to gili air
Other way is using fast boat to gili air from Bali. There are many fast boat to gili from Serangan, Benoa or Padang Bai that are operated daily. Those fast boats will bring you straight to Gili Air, Gili Trawangan and Lombok.