Get an Octopus Card and use the MTR system
Much of the city is served by the MTR, an ever-expanding network of clean and efficient train lines. For the majority of your navigating needs in Hong Kong, you'll want to use this. Taxis are available, but they can be expensive (especially for cross-harbor journeys and at night).
The traffic condition in the city is likewise notoriously bad. Trains run every three minutes during peak daylight hours, and stations are safe, large, air-conditioned, and crammed with shops. Simply make a cash deposit, purchase a pre-paid Octopus Card at any MTR station customer service kiosk during working hours, and swipe in and out for each ride. The costs are determined by how far you travel within the system, albeit it is by far the most expensive option.