Transfers

You may have better luck getting useful replies by posting this in the England forum and using a more informative subject line. But I can answer your questions:

The "transfer" is not a physical piece of paper - you just get off one train and get on another. You'll have to change platforms, though, so when you get off the Piccadilly line at Piccadilly Circus, look for signs to the Bakerloo line and follow them.

In general, it's not very time-effective to use hop-on-hop-off buses in London as your main way of getting around. The main sights are spread far apart, and London traffic can be very bad. The tube is a much faster way of getting from place to place, so you may want to learn more about it before your trip.

Oyster cards are no trouble to use at all. You just tap your card at the fare gate at the station where you get on the train, tap again at the fare gate where you exit, and it will automatically charge you the correct fare. The nice thing about London's system is that they have "fare capping." This means that once you take enough trips in a day to equal the cost of a day pass (maybe plus or minus 50 pence - I forget), it stops charging you, and you can ride for the rest of the day for free.

Maybe it would make more sense to you if you use the word change instead of transfer. You are simply changing from one train to another. (Like changing airplanes in the airport) The most important thing for you to know is the end station for your line. In others words, if the train runs between A and J and you want to go from C to G, then need to catch the train headed to J. The J stop will be shown on each car and the head of the train as it pulls up to the platform. There will be signs and large boards that lists all the stops from A to J and another board listing all the stops from J to A. That way you always know you are headed in the correct direction. And another thing I always do is focus on the stop before. If I want to get off at G, I look for the F stop, so I know that the next stop is where I want to get off and I am prepared. And if you blow it by missing a stop, it is not a big deal. You get off at the next stop, follow the signage to the other side and ride back one stop. All that you have done is to lose a little time.

And the hop on/off buses is a good idea for an orientation and getting to principle sights but a poor choice for using as public transit. The oyster cards simple and easy to use. Just make absolutely certain that you check in and OFF the train. In most location the card is needed to activate the entry or exit gates. In some of the newer stations there are no exit gates so watch what the locals do.

This is a duplicate post. I have put my answer at the other copy, here: https://community.ricksteves.com/travel-forum/general-europe/transfers

I hope you understand that the Underground is zoned and prices vary according to destination. The Oyster card automatically deducts the correct fare at your exit, assuming of course it holds enough money for the trip.
I think you will find the hop-on-off bus good for early orientation but really slow for basic transport. The Oyster card has a top limit per day and after that you effectively ride free for that day. Easy. But to repeat, you use it twice, once to enter the Tube and once to exit. https://tfl.gov.uk/travel-information/visiting-london/visitor-oyster-card