The London underground, or “tube”, carried a reported 1.1 billion riders last year. London buses (where everyone, including hardened Londoners loves to sit in the front row on the top floor of a double-decker) carried 2.2 billion people.
The best, and cheapest, way to use both services is a smart card called an Oyster. Basically, you buy (actually, rent) the card for £5, then buy credit on top of that and every time you swipe the card, getting on/off the tube or bus, your credit is reduced. Everyone loves their Oyster.