Hong Kong's public transport is excellent — fast, cheap, and comprehensive enough that a car is a liability rather than an asset. The key tool is the Octopus card, a rechargeable contactless card accepted on the MTR, all buses, trams, ferries, and most convenience stores. Pick one up at any MTR station for a HK$150 deposit (HK$50 refundable).
The MTR (Mass Transit Railway) covers most of Hong Kong Island and Kowloon with frequent, clean, air-conditioned trains. The Island Line runs along the north shore of Hong Kong Island; the Tsuen Wan, Kwun Tong, and Tung Chung lines serve Kowloon and connect to the airport. The East Rail Line runs up through the New Territories to the mainland border at Lo Wu.
Buses are extensive and reach areas the MTR doesn't, particularly the south side of Hong Kong Island and the New Territories. Route numbers and destination boards are in both Chinese and English. The bus network is bewildering at first but route information is available on the MTR app and transport department website.
The Star Ferry crosses Victoria Harbour between Tsim Sha Tsui and Central (or Wan Chai) every few minutes. It's the most scenic way to cross and cheaper than the MTR tunnel. Outlying island ferries depart from the Central Ferry Piers; services run to Lantau (Mui Wo), Lamma, Cheung Chau, and Peng Chau throughout the day.
Trams (double-decker, very slow) run along the north shore of Hong Kong Island from Kennedy Town to Shau Kei Wan via Central and Wan Chai. Cheap and good for short hops or sightseeing.
Taxis are plentiful and metered. Urban taxis are red; New Territories taxis are green; Lantau taxis are blue. Drivers often don't speak English — having your destination written in Chinese characters helps.