By bus
Since the opening of the Lantau Link, a number of buses also cross over to Lantau, although they are considerably slower than the MTR and less scenic than the ferries.The local bus timetable in Lantau island is available online. (http://www.newlantaobus.c...)
There is an extensive bus service from the rest of Hong Kong to the airport and Disneyland.
By car
Whilst you can drive your car onto Lantau, the road system is limited and much of the island is zoned as a country park and is off limits to normal vehicles. If you really want to see Lantau you should get out of your car. The Disneyland is however still accessible by car and connected by the Lantau Link expressway.
By train
The Tung Chung MTR line is the fastest way to get to Lantau if you are going to the north of the island. The Tung Chung line also connects with special rail services at Sunny Bay that take visitors directly to Disneyland. The trip to Tung Chung takes around 25 minutes all the way from Hong Kong station and costs $18-20.50. Children 11 years and under enjoy a 50% discount.
From The Airport
Lantau Island is adjacent to Hong Kong International Airport, the airport island is linked by two short bridges. The best way to Lantau from the airport is either by taxi, by bus, or by foot. There is no train service from the airport to Lantau, although there is an indirect service with the Airport Express train and the MTR via Tsing Yi. The premium charged by the Airport Express train for this trip will likely make it more expensive than a taxi if there are two or more people travelling.
Taxis from the airport to anywhere in Lantau are relatively fast and pleasant, but only light-blue taxis are allowed on the island. Ask at the reception desk at the airport taxi stand to call for a light-blue car for you. The more common red and green ones are prohibited to go to Lantau.
Alternatively, there are frequent buses that travel towards Tung Chung MTR station, including S1 and S64 from the airport terminal. Although you can use the A35/N35 for travelling to Mui Wo directly from the airport, the frequency of this particular route is sparse. It's usually better to change on to local buses at Tung Chung MTR interchange, where you can find buses to most destinations across Lantau island.
It's a about a 5km walk from the airport to Tung Chung. The main northern bridge is a highway that doesn't allow pedestrians, but there is a nice walkway over the southern bridge from the airport to Lantau.
Discovery Bay
Situated on the north-eastern coast of Lantau Island, Discovery Bay is accessible by 24-hour ferry from Central District in Hong Kong Island or by buses from Tung Chung new town, Sunny Bay MTR metro station or from the Hong Kong International Airport at Chek Lap Kok.
Timetables for bus and ferry services:
Bus (http://www.hkri.com.hk/ic...)
Ferry (http://www.discoverybay.c...)
By ship
The obvious way of getting to the island is to take a ferry. Ferries depart from the Outlying Islands pier in Central, to the west of the Star Ferry terminal. The largest operator is the New World First Ferry.
Discovery Bay: Pier 3, $31 fast only, every 10-30 minutes.
Mui Wo: Pier 6, $13.00 slow / $25.50 fast, every 40 minutes.
Ferries to the island, as well as buses, impose a 50% surcharge for travel on Sundays and public holidays with the exception of services to/from/within Discovery Bay, Disneyland and the airport. It's cheaper, and less crowded, to visit during the week or on Saturdays.