Octopus card. Buy one at any MTR station. It covers the MTR, buses, minibuses, trams, ferries and the Peak Tram, and works in convenience stores, supermarkets and a great many shops. Contactless bank cards now work on the MTR but not everywhere else.
MTR. Ten lines, every two to four minutes, air-conditioned, bilingual signage, roughly 6am to 1am. Fares are distance-based and cheap. Note the lettered exits — large stations are enormous.
Star Ferry. Across the harbour in ten minutes for a trivial fare. The best value in the city.
Trams. Double-deckers along the north shore of Hong Kong Island since 1904, at a flat fare of a few dollars, paid on exit.
Buses cover what the MTR does not, including the Peak and the south side. Green minibuses run fixed stops; red minibuses stop on request and you shout.
Taxis are colour-coded — red for urban areas, green for the New Territories, blue for Lantau — and a red taxi cannot serve a green area. Have your destination written in Chinese. Many take cash only.
Airport Express reaches Central in 24 minutes with free hotel shuttles and in-town check-in; the A-buses cost about a fifth.
Escalators and walkways do a great deal of the pedestrian work, including the Mid-Levels Escalator, which runs downhill until 10am and uphill after.
For the detail, see Getting Around Hong Kong.