From the airport in Malta you need to go to the ferry port Cirkewwa, where every 45 min goes a ferry to Gozo. The way to the ferry takes around 60 min by bus or 40 min by taxi. If you like to rent a car I recommend to do so from a Gozo car hirer. Most of them offer the transfer to the airport as well. I also recommend to book the Taxi or hired car as soon as you have booked your accommodation since rented cars in summer often are booked up.

The transfer to Gozo with the car ferry takes about 20 min.

From the ferry port to Fort Chambray it's about 1 km. By taxi it's just 5 min, by bus it's 10 min, bus stop "Fort Chambray". If you have light luggage you can walk within 20 min (800m uphill).