The easiest way to move around this huge city is the underground. London’s tube covers 9 zones and it has 12 lines that can bring you everywhere.
To save some money, we highly recommend you to buy the Visitor Oyster Card before moving to UK. It is an electronic ticket that you can charge with money at every station (or when buying it). Using the Oyster you can have some discounts on each journey. This ticket also offers discounts for some restaurants, shops and attractions.
If your trip to London is longer, also have a look at the Travelcard option, a paper-pass valid for a few days or weeks on the zones you choose.