In London the metro will take you almost anywhere, but even without the metro you could easily get around using the bus. It is worth knowing that children between 5-10 years can travel for free with public transportation, 11 year old children as well, but they need an Oyster Card ID with picture.
The single ticket for the metro costs £4.50, the tram and the bus ticket £2.30. With one metro ticket you can change lines as much as you want, but that is not true for the bus ticket. To read more about the prices and zones, visit: http://www.tfl.gov.uk/tickets/14416.aspx
If you would like to travel cheaper, you might want to invest in an Oyster Card. This is a discount card, possible to buy on some locations. With this you will get a nice percentage on for example bus and metro tickets. It is worth using, at least if you plan on spending some time in London. You need to validate it as you enter into the metro system, and as you leave the metro. More information: http://www.tfl.gov.uk/fares-and-payments/fares?intcmp=1648
TravelCard is a ticket which can be bought for a day, a week or even a year. When this is paid you can travel unlimited amount of times with metro, bus and tram (depending on for what zones you bought the travel card). It is possible to buy an “Off-Peak TravelCard”, if we only travel after 9.30. More information can be found at http://www.tfl.gov.uk/tickets/14416.aspx
The Buscard can be bought and be used on all buses. In 2012 a one week buscard costs £18.80. If you have the Oyster Card this gets a bit cheaper. More information can be found at: http://www.tfl.gov.uk/tickets/14415.aspx
If you buy the London Pass you can visit 55 attractions for free, and you do not even have to stand in line. Other discounts are also available for those with a London Pass, so for tourists, this is worth buying. More information, description and online purchasing: London Pass