You can either take the London Underground. The big attraction is price, frequency and speed.
Expect to pay £3.10-£5.10 One Way
Buy Train Tickets to Heathrow Airport
The Paddington Heathrow Express Train is a dedicated rail link into Central London.
Expect to pay £8 - £22 (one way) depending on how far in advance you book
Book Cheap Train Tickets to Heathrow Below