The easiest option is to take any bus beginning with A or E to the Lantau Link Interchange. This is the first stop after the long stretch of highway upon leaving the airport area. Use the tunnel walkway to cross to the other side of the road, then take bus R8.

It will cost you approximately HK$20 to $40, as the buses have different fares (in Hong Kong you almost always pay to the final destination of the bus regardless of where you get off). Bus R8 may be free or discounted, when you have used a non-cash method to pay for certain A and E buses in the past hour (sometimes 2 hours).

The E buses are marginally slower as they go round the airport offices and/or nearby commercial/residential areas first. The A buses are slightly more expensive.

There is no easy way to see the fares for all possible routes without tediously checking them individually. This unofficial site has the information about discounts in Chinese, but nobody has yet volunteered to translate it on the English version of the site. https://hkbus.fandom.com/wiki/%E8%BF...7%9A?so=search


It is possible to take the train with 2 changes. From the airport, you would first go past Disneyland (but you won't be able to see it - you might see the Mickey trains) to Tsing Yi. You then have to leave the station, go to another level and re-enter the station to take a different line that backtracks along the same route. Then change at Sunny Bay for the Disney line. This normally costs HK$65, but you can buy discounted tickets on websites like Klook.