What is the fastest and cheapest way to go to Lantau Island if I would be coming from Tsim Sha Tsui?

Well, the island is a large area. So take Mui Wo (a village on the island) as an example, take Tsuen Wan Line to Central Station. Then walk to Central Pier No. 6 to take a ferry to Mui Wo Ferry Pier directly. The whole way takes around 95 mins. It costs 24.6 HKD per person.