Public transport in London is not too hard to get to grips with if you are staying for an extended period. However, if you've only got a week, you should try to orient yourself before you get there! Have a look at the Transport for London website at for maps, prices, etc. They also have a great journey planner that has been my guide for the past year. I've gone over some of the basics of travel in London below.
London is divided into 6 travel Zones. It's easiest to think of a giant circle, with Zone 1 being a patch in the centre, and Zones 2-6 radiating outward. Most tourist attractions and major hotels will be in Zone 1 or 2.
First off, I'll say you MUST get a travelcard to do sightseeing. It's almost guaranteed that the amount of travelling you'll do will make the cost of a travelcard a bargain. You can buy them daily or weekly, depending on the length of your stay. If you buy a daily travelcard on weekdays, make sure you do it after 9:30am, otherwise you'll be charged more for peak use. If you buy your daily or 3-day travelcard in advance, ask for an off-peak and plan not to travel until after 9:30. Weekly travelcards do not have this restriction, but best to leave peak time to the commuters anyway. If you want to be really cheap, buy a bus pass. It might take you longer to get places, but you'll see more and avoid the Tube.
Travelcards can be bought from machines at rail or Tube stations, or from ticket windows. Some machines will take credit cards.
Types of Transport:
1. Buses: Central London buses are now pre-pay, you can get tickets from the machines at each stop. Better yet, buy a bus pass for unlimited journeys. Daily bus passes are available from the machines.
2. Underground Rail or "Tube": Made up of several different "Lines", can usually get you to any major tourist attraction. Travelcards are a must, make sure you have the appropriate zones to get where you're going (see "zone extensions" under the Overground Rail section).
3. Docklands Light Rail (DLR): Exclusive to East London, plenty of links with the Underground. You can also use travelcards, provided you have the right zones.
4. Over ground Rail (also "National Rail", "British Rail"): If you're sticking to London for your trip you probably won't use these trains much besides the journey from the airport. Travelcards are also good on these, but make sure you're only going within the zones you've paid for. For instance, if you have a zone 1-2 travelcard and you want to take a trip out to something in zone 4, you will need to buy a "zone extension". At the ticket window you should say you need "a zone extension from zone 2 to zone 4, return". You will get two tickets, one for your outward journey and one for coming back, only good on that day.
5. Taxi: Taxi stands are all around the city, major stations or hotels will usually have them. Try to avoid using cabs if you can, as they are very expensive. You are not expected to tip (they carry change). Black Cab drivers are famous for having "The Knowledge", meaning they studied London geography extensively and should know the fastest way from point A to B better than anyone. Despite this reputation, I've twice experienced drivers who either really had no clue, or pretended they didn't so as to charge more. Don't get into the cab until you've told the driver where you want to go and confirmed that they know the location and are willing to go there.
Top Tips for using public transport:
Double decker buses are great for cheaply seeing the sights. The Number 11 goes by almost as many sights as the tour buses and only costs one pound twenty pence. However, they are very hot in the summer (no a/c) so you won't want to stay on for long. Make sure to bring water with you.
Tube during the summer is also very warm and sticky (again no a/c). Bring water, and get off to get some air if you feel ill.
Don't give your used tickets to the "touts" in or outside stations. It's illegal and could get you into trouble, and these people are basically scam artists looking to make quick cash buy selling your ticket on to someone who is stupid enough to buy it.
Keep your travelcard somewhere on your person where it won't get lost, but it is easily accessible. There's nothing more irritating than getting stuck behind someone who is searching for their ticket!