Get the weekly Travel card once you’re in London. Pick up an underground map and plot your journey. A bus route map is harder to find but you’ll get good use out of it.
This comes in really handy. Once inside the train, an automated announcement reaffirms what train you are riding, its destination, then what the next station will be and what connections can be made from there. Platforms and trains can get very crowded, even outside of rush hour which seems to last about two hours. 
In fact, at some stations, the numbers of people entering can be restricted at times and you may arrive to find a guard stopping your way in. 
While you’re waiting for your train, you can buy candy, chips, pop and magazines from the kiosks and sometimes baked goods and lottery tickets. On the platforms you’ll also find candy machines. Travelling on the underground is hardly boring but there are so many stations and so many announcements, your journey can sometimes seem very long.
Discover the buses if you can. Most are double decker but not all. Going upstairs can be a challenge in a moving, lurching bus. Take your time, especially coming down! We eventually found an All London Bus Route Map. It was invaluable. We also discovered that certain routes took us past lots of sights. Who needs a tour bus! Look for the number 11 (the route is on the left) and the number 8! On the newer buses, pay the driver. On the older buses, a conductor will come around to check passes and sell tickets. The cheapest fare is 60p and it won’t get you very far. Traffic in London is congested and the roads are anything but straight, but you’ll see so much more by travelling this way, if you can spare the time.
On this trip, I also rediscovered the overground rail system. It covers more ground more quickly than the underground but it skirts the city rather than going through it. Sometimes this was a better way to travel. The underground can get claustrophobic. Just as in the underground, there are train announcements to help you out. Everything feels very organized. We even saw some bus stops with digital displays about the buses due to arrive there.
TIPS: Get the weekly Travel card once you’re in London. Pick up an underground map and plot your journey. A bus route map is harder to find but you’ll get good use out of it.
If you’re staying in London for a while, consider buying the travel card that the residents do. It will work out more cheaply than the tickets you can buy before you leave your own home, or at least allow you to travel at any hour of night and day and on any transportation method you choose. You’ll need to present a passport sized picture. In many train stations (underground and otherwise) there are photo booths that are perfect for the job. If you’re staying in town and mostly looking at tourist attractions, a Zone 1 ticket might be enough, or consider a Zone 1&2. Not too many things are further afield. We are staying in Zone 4 so have to buy a Zone 1 through 4 ticket.
You’ll get a plastic wallet one side holds your photo ID card and the other side is where your ticket sits. On buses, just show the ticket. On
the underground, most stations have ticket machine. You push your ticket into a slot and it comes back out of a slot on top. Take your ticket back to use again and the turnstile will let you through. On some underground trains and on the surface routes, you won’t have to produce your ticket at all but be prepared. There are spot checks and it will cost you £10 if you’re caught travelling without the correct ticket. On the whole, there’s an amazing honour system and it seems to work.
Now, I'll tell you about travelling out of London: