Subway, or Tube in London term, because the subway looks like a tube. Once you get to the tub station, one option is to buy an Oyster Card (the Pay as You Go Oyster Card). You prepay fares when buying card. Typically, each trip within central London costs about £2.2 (2.2 pounds). So you'll need to estimate how much prepayment to put in.
You can find more information at http://www.tfl.gov.uk.