The simplest thing, Ilovemarkb, is to do what the majority of Londoner's do and use an Oyster card. (It still seems to be far more commonly used than the newer contactless technology).
You can buy it online (and then pick it up at a station) but it's probably simplest (since you won't need to create an account) just to buy one from the Underground ticket office of your arrival station in London. You pay £5 (refundable) deposit for the card plus whatever amount of credit that you want to put on it.
As long as you won't be travelling outside Zone 4 (which, based upon your various posts here, seems to be very unlikely), or travelling before 0930 on a weekday, the maximum cost of your travel is capped at £8 per day. So (for 2 days travel, plus the cost of the card) you'll need to pay £21; that will cover you for unlimited bus or tube journeys in Zones 1 to 4.
You simply touch your card on a reader by the entrance and exit gates on the Tube. On a bus you touch your card on the reader by the door when you get on only.
At the end of your stay you can either keep the card for future use or get a refund of the cost of the card and any unexpired credit. (You can do that at any ticket office or, where the available credit is less than £10, at ticket machines).