If you're from out of town, London is one of the most expensive capitals I know for public transport. A tube ticket now costs $4 even if you're just going two stops. (By comparison, in Paris, I pay EUR 1.80 for any trip on the metro.)
The way round this is to get yourself an Oyster Card. You can get one at most tube stations and national railway stations. You need to fund it with $3, at least (Oysters can store up to $90), and you can top it up over the internet or at a station. (If you're living in London for a while you can also use the Oyster to load up your season ticket.)
When you're using the Oyster Card your fares will be cheaper - $1.50 instead of $4 for the tube in Zone 1. The system also keeps a running total of how much you use a day, and if you would have been better off buying a one day travelcard, at that point it will stop charging you for your journeys. So you are guaranteed to do better with the Oyster.
You do need to remember to "touch in" and "touch out" at each end of your journey. But apart from that, using your Oyster is pretty easy.
The Oyster Card also gives you access to some useful discounts on visitor attractions and shows, such as a 2 for 1 offer at Monty Python's Spamalot, 25% off the bill at some restaurants, and even a 2 for 1 offer on the Fullers Brewery Tour. Check these out at Oyster Offers.