You can either take a cab or use the public services. To start with, you can have a look at a map of the City . The public services in London include the Underground, the buses and some railway lines.
Public transport is privatised in Britain.
The public service plan in London is divided into zones. Obviously, this area includes the lion's share of tourist attractions, and a fair amount of accommodation as well. The higher-numbered zones form concentric rings, each of a few miles, around the center. Heathrow Airport is in Zone 5. By the way, some stations are exactly on the boundary between two zones.