In the center of London there are a few forms of public transportation: Tube, Bus, Bike.
One of the first things that you should do when arriving in London (or even before arriving to London depending on how organized you are) is to get an Oystercard. This can be done a couple of ways:
at a tube station
at certain local shops (just look for a sign out front with the logo).
To learn about the most convenient place for you to get your Oystercard as well as information on the additional Travelcard and Bus and Tram passes look here: https://tfl.gov.uk/fares-and-payments/where-to-top-up-and-buy-tickets
Although paper tickets exist, they are hardly realistic. A journey with a paper ticket often will end up costing you more! Oystercards and contactless cards can be used for pay as you go fares. Depending on your transportation use, this may be the most cost effective option for you. They can be used on the Tube, bus, DLR, Overground, TfL Rail, Emirates Air Line, River Bus and many National Rail trips.
Pay as you go fares have a daily cap, which depends on the transport types you use. For example the Zone 1-6 cap is 12 pounds while the Zone 1 cap is 6.60 pounds. If you travel only twice a day on the Tube everyday it is recommended that you use pay as you go rather than a 7 Day Travelcard for the cost savings.
For others, 7 Day Travelcards may be more cost effective if you travel over four days a week. The 7 Day travel card works for unlimited travel if your travel includes Zone 1. They can be purchased at the Tube ticket machines or from Overground or TfL rail stations. Travelcards can also be bought online in advance.
In general, peak hours on all services other than the bus are from 6:30 to 9:30 in the morning and 4:00-7:00 in the evening. This is when rush hour is, so tickets are more expensive.
During the workweek the tube closes at varying times depending on the line, however they do not run all night. During the weekend certain tube lines have night hours, however the tube may not stop at every stop. When going out at night be sure to know how you are getting home. Nothing kills a night like a £50 taxi fee.
It’s worth noting that the tube can be very warm in the summer (and even during the winter), so make sure to remain sufficiently hydrated throughout your journey.
To learn more about the one way fare of you trip click here: https://tfl.gov.uk/fares-and-payments/fares/single-fare-finder?intcmp=1660
You must have an Oyster card or a Contactless to pay for a bus fare, they do not take cash. There are hopper fares when you make two journeys on a bus or tram within an hour which makes the second trip on the bus or tram free provided you do not take any other form of transport in between the two bus fares. If you don’t have enough credit on your Oyster card to pay the fare or your Travelcard has just expired, it’s possible to make one more journey on the bus despite the lack of credit.
If you prefer the bus or the bus is your most convenient form of travel, it is possible to purchase a 7 day bus and tram pass. This can provide cost savings if you make over 14 trips a week on the bus or tram.
There are a lot of moving parts to the prices of public transport in London, so take a look at the website to learn more! https://tfl.gov.uk/fares-and-payments/
To learn more about caps: https://tfl.gov.uk/fares-and-payments/oyster/using-oyster/price-capping
If you are up for a bit of a challenge, Santander bikes are a third option of transportation. There are bike ports on many street corners in London. For casual bike users you will need to have a credit card or debit card in order to take out a bike. This pay as you go method can give you 24 hour access to bikes for just 2 pounds, just keep the ride to less than 30 minutes increments . If you use the bikes regularly you should look into becoming a member for 90 pounds a year.
To learn more details on how it works see here: https://tfl.gov.uk/modes/cycling/santander-cycles/how-it-works