Heathrow is a very well connected airport, with 3 tube stations, and 3 rail stations within the airport boundary.
Terminals 4 and 5 each have a tube and train station each, the remaining stations connect you to terminals 1,2 and 3.
Hatton Cross tube sits to the east of the airport, just outside the boundary fence on the final approach to runway 27 Left. This station is serviced by buses which will take you to various areas in and around the airport, and is a great place to plane spotters to enjoy low, slow aircraft landing on 27L.

Getting to Heathrow by Train.

Heathrow from London.

The Piccadily line will take you to Heathrows terminal stations from central London.

Heathrow Connect is a fast cost effective way to get to Heathrow, from Paddington Station, and goes to the train stations servicing T1,2,3 and T4.

Heathrow Express will get you from London Paddington to Terminals 1,2,3,4 and 5 stations in 20 minutes, pricier than Heathrow Connect but much quicker.

From outside London.

Heathrow can be accessed by train eitheby entering London and using the options above, or by connecting at Feltham, Reading, Woking and Watford Junction.

Heathrow Train Times