There are dispensers where you can buy Oyster cards in a lot of the tube stations (think they're £3 or so). Some flights also sell them on the way in these days with pre-loaded credit.
The card will work on the tube, buses and a lot of the national rail services within London - national rail services going out of London are a bit of minefield pricing wise so you're better off asking at the station for the cheapest fair at the time you are travelling.
The cheapest way to get around London is to buy a 7 day travelcard and have it loaded onto the Oyster card at the machine/kiosk, you probably only need zone 1 depending on where you're staying.
(P.S. I would agree with visiting the British Museum and the Science Museum; the National History Museum is an amazing building and the dinosaurs are cool but the rest of the exhibits are a bit boring, however it's next door to the Science Museum and they're all free so you might as well stick your head round the door.)