London is big and, while you can, of course, walk to most places, it sometimes might be more convenient to take the public transport. The good thing about London is that the public transport works great and can get you anywhere, in several ways.
If you’re Dutch, like me, you might think of the Oyster card as an OV-chipkaart. The only difference is that this card is only for London and not for entire Great Britain. If you’re not Dutch, the best way to describe the Oyster card is: “Oyster is a plastic smartcard which can hold pay as you go credit, Travelcards and Bus & Tram Passes. You can use an Oyster card to travel on bus, Tube, tram, DLR, London Overground, TfL Rail, Emirates Air Line, River Bus services and most National Rail services in London.” 
You can buy a visitors Oyster card at any ticket machine or buy a personal Oyster card online when you live in London and for example want to add a certain discount to your Oyster card or want your credit to top up automatically using your credit card.
It, of course, is also possible to buy tickets, but these are about 40% more expensive, so an Oyster card might be the cheaper option if you’re in London for more than a day.
There are several discount cards which you might benefit a lot from when you stay in London for at least a year. These are the discount cards available :
- 16-25 Railcard £30,- per year
- Two Together Railcard £30,- per year
- Family and Friends Railcard £30,- per year
- Senior Railcard £30,- per year
- Disabled Persons Railcard £20,- per year
- Network Railcard £30,- per year
All the cards have different advantages; make sure you find out which discount card is most beneficial for you. Once you’ve received your discount railcard you can connect it with your Oyster card by going to an underground ticket desk and asking them to do so. There, unfortunately, is no other way to connect your discount card to your Oyster card.
There are four main kinds of public transportation possibilities, first of all, the bus. When you take the bus it doesn’t matter how far you go, you’ll always pay the same price: £1.50. You tap in at the front of the bus with your Oyster card and take a seat, easy as that. Every bus has an electronic sign that will tell you in which bus you currently are and what the next stop will be. Most buses also have a nice lady voice that will tell you, about halfway between two stops, what the next stop will be.
Buses are available everywhere in the city; make sure you check whether your bus is going in the right direction because they drive on the left 😉
London does not have a lot of trams; there are only two lines and they run between Beckenham Junction and Wimbledon. 
Tapping in with your Oyster card works almost the same as in the bus, except that you don’t tap in inside the tram but on the platform. For the tram you’ll also pay £1.50 per ride. You can also buy a ticket at the ticket machine on the platform, this is more expensive though.
The train network in London is amazing! It can take you from the one far end of London to the other and lots of train stations in London also have trains that can take you outside of London. The stations where you get on the train usually have gates, by tapping your Oyster card or putting your ticket in it these gates will open and you may enter the train station.
London is divided into zones; the amount you pay depends on how many zones you travel through. It also depends on what time you are travelling, especially when you have a discount card. You pay less during off-peak hours and sometimes extra during peak hours when you go into the city centre.
Apart from the trains, London is also very good connected by the underground network. It’s just as easy as taking the train and the payment is the same. The only difference? All the seats are sideways and it’s underground. The tube also might be a bit hot so zip down your jacket or enjoy the warmth if you were freezing during the winter. 
With all these possible ways of transportation it might get a bit complicated, but don’t worry! With the app ‘citymapper’ you will easily be able to find out which route is either the fastest, cheapest, gives you the best view of the city (buses only) or is rain safe.
The only thing you have to do is type in where you are at that moment and where you want to go. You can even use GPS so it can just use your current location when you don’t know where you are exactly or what the place is called. 
Enjoy your London travels!