You can get to Discovery Bay either by ferry or by land.
Firstly there is the very comfortable ferry ride between Central Pier 3 (near IFC) and Discovery Bay which runs around the clock. The ride takes about 25 minutes and you can even get free Wi-Fi on board.
There are also frequent regular shuttle bus services running between DB and Airport, Sunny Bay MTR station and Tung Chung MTR station. The bus ride takes about 20 minutes.
DB also runs a VIP limousine service that provide door to door service between DB and anywhere in Hong Kong (call 29871213 for booking). For example, they can pick up your family from the Hong Kong International Airport or any hotels in town.
It is understood that application has been submitted for allowing Taxi service into restricted area in DB (right now pick up is only outside the tunnel) but it is still pending Government approval at the time of writing.
Access DB operates a rahabilitation bus for barrier-free transaportation for the handicapped, sick or elderly. Anyone with a genuine need can book the bus, be picked up at their doorstep and taken to their destination wherever it may be.
Some residents do however keep a private car in Sunny Bay Government carpark, or even Tung Chung, to enjoy at weekends, or even commuting to less accessible areas of Hong Kong.