How to get around London on a budget?

Getting around London can be an expensive activity. When you have a limited amount of time and want to see as much of the city as possible, it is impossible to avoid all expenses.
Nevertheless you can try to choose the best travel option for your type of trip.

Arrival
The usual arrival to London is through one of its airports. You can easily spend a fortune on a ride to the city center. If you plan in advance, you can do the same for as little as £2.
I have devoted a whole post to this topic. If you want to know more, you should check out my advice on how to get from airport to central London.


Walking...
...is definitely the cheapest way to move around the city center. You can definitely walk between some of the famous sights and see the city at the same time. Tube is a great thing but you don't get to see all that much while underground.
Remember: your journey can often be the highlight of a trip, it does not necessary mean reaching the destination itself is the thing.

Renting a bike
There is a number of bicycle rental companies around London. If this seems the right thing for you, you should check out Barclays Cycle Hire.
If you use the system the right way, you can get away with paying as little as £5 per week. That is how much you have to pay in advance - renting for up to 30 minutes is free.
However you should be aware London is not the friendliest city for cyclists out there. There are not all that many bicycle lanes in the city center. Since pavements are reserved for pedestrians you will often have to use the bus lane.
You should also keep in mind driving on the right side of the street. As you should know, in UK the right side is actually the left.


Do you like Oysters?
Well even if you don't, I suggest you get yourself an Oyster Card as soon as you get near a Tube station (Americans would probably call it a subway station).
You can use Tube, DLR, London Overground, Bus and tram, National Rail and some riverboats using an Oyster Card and pay roughly half the price you would have payed using cash (actual ticket prices are available here).
There are roughly two options for using an Oyster card. You can load a travel card onto it, or load some cash and pay as you go.
You should consider both options and choose one depending on how much will you be moving around. For instance if you plan to use the Tube for 5 to 7 days, you should probably choose the 7-day travel card.

Moving around using the Tube is the fastest way. It is actually a bit like a teleport - you get quickly from point A to point B but don't get to see anything on the way.

Check out the Transport of London webpage for up to date London traffic info and prices.
They offer a useful Journey Planer for free. Try it out, it might come in handy.

Another very useful resource with loads of information on London is Visit London.

There are also other transport alternatives... like for instance riding in a Cycle rickshaw. I actually saw quite a few of those.
If there is another transport option I left out, please do not hesitate to comment.