Coming from Heathrow, the least expensive is the London Underground, at 5.70 GBP cash fare, lower if you purchase and use an Oyster card. Journey time is between 75-100 minutes depending on time of day and which terminal you start from. There is one change of underground lines.
More expensive but faster is the Heathrow Connect train; total journey time would be about 40-50 mins and cost would be 9.90 for the train and another 4.70 for the underground (less if you purchase and use an Oyster card).
More expensive still is the Heathrow Express, with a shorter total journey time, but a higher train fare.