What's wrong with this explanation for tourists:

An Oyster is a little card that you touch in and touch out the gates
with. On buses, you only touch in. Get a PAYG one and you do not have
to worry about how much it costs. It will be the cheapest way for you
to get around. A trip will cost you 1 pound on the bus, and one fifty
on the tube. Put enough money on the card to make sure you can travel
around. You can check your balance at every station using the machine.

I wouldn't go into zones, peak/off peak and the slight bit of money
they might save using other kinds of tickets.