London is, above all, a walker's city, and will repay every moment you spend exploring on foot. But if you're in a rush, there are other options. By far the easiest and most practical way to get around is on the Underground, known as the Tube. Trains run daily from early morning past midnight during the week; beginning in late 2017, six key lines will operate 24 hours per day on weekends. Frequent cash-free buses crisscross London and often have their own lanes, which only buses and black taxis can use. They are a great way to see London, but navigation can be more complicated than the Tube's; scan the route posted at the bus stop and check the number and destination on the front of the bus, and ask the bus conductor if in doubt.
Put a deposit on an Oyster card for £5, which will allow you to use London's transport—including bus, Tube, tram, DLR, London Overground, and most National Rail services in London—at a lower cost than using paper tickets. The plastic card can be topped up as often as you want, and your £5 deposit will be reimbursed when you hand the card back.
Alternatively, buy a Travelcard pass (from £12 per day in the central Zones 1 and 2), which offers unlimited use of the Tube, buses, and the commuter rail. Check www.tfl.gov.uk for details on ongoing Tube renovations.