Hello,
There are various forms of public transport available in London. You can choose which is convenient for you that suits your journey.
Trains
Tube (Underground)
Buses
Taxis
DLR (some may call it Metro)
Bicycle
Riverboat
You can obtain a small pass, size of a credit card. Known as an an Oyster card, you can use on the Trains, tube or DLR, you can use this same card on the buses too. However, if you purchase a bus pass oyster card, you cannot use this pass for the Tube, trains or DLR. There are different pricing structures for Trains, Tube and DLR. You can either purchase a weekly, Monthly or yearly pricing plan. the same applies to a bus pass oyster card too (weekly, monthly and yearly). They also do Pay as you go cards too. See link below for more details;
http://www.tfl.gov.uk/
Trains
Trains runs overground and are frequent from Monday to Friday. They start as early as 6:00am in the morning till 12:00mid-night. Sunday the service is reduced and trains are less frequent. Train fares are generally expensive compared to buses. The further you travel, the more expensive the fare gets. I dont believe trains in London are air conditioned (they only have small fans which you control manually), but i do know
they have heating for the winter season.
During the working week (mon-to-fri) 7:00am to 9:30am and 5:00pm to 7:00pm trains will generally be full taking passengers to and from work. This is known as the rush hour or peak time!
Tube
The tube running times are roughly the same as for the trains or maybe they start just before 6:00am. Tubes mainly run underground and operate mainly in London where they have zones. they start in Central London (zone 1) and terminate at zone 6. To get a better idea of zones and how the tube station is laid out, please see link below ; The tube system is expensive compared to buses but will get you from A to B relatively quickly. The same applies to the tube system with regards to the rush hour timings. In winter, the tube system is nice and warm. However, in summer, the temperatures soar making the journey abit uncomfortable as i don't think the tubes are air conditioned.
http://www.tfl.gov.uk/gettingaround/1106.aspx
DLR
This form of public transport is not as fast as trains or tubes but faster than buses. The payment of using this system may be similar to train and tube prices. The DLR network is smaller than the tube and rail system although in recent years, the DLR network is expanding.
Buses
The buses are slower than the trains and tube system but people use them as its a cheaper form of public transport. Although now in central London and going on the outskirts of central London, bus lanes have been introduced that give buses priority over other vehicles on the road. Buses are generally uncomfortable when full as there is no air condition (although few new buses have air cons now :-) ) and the journey is slow during peak times due to traffic.
Taxis
Taxi prices depend on where you live in the UK. I'll just generalize in central London with regards to black cabs. These black cabs "trade mark of London" generally circle around central London and can be flagged down at any time in the street providing they are vacant. They normally have an amber light "for Hire" lit when ready to hire. These cabs are costly and the meter runs as soon as you board the cab. These cabs are licensed and probably safer at night for use if traveling late. You normally find these cabs operating in Central London, Airports and in some parts of Uk outside train stations. Fares vary as i've only used them in central London occasionally.
Bicycle / River boat service.
These services are newly introduced in London, especially the bicycle one. Again you can use your Oyster card to hire these bikes. No paper work involved just swipe your oyster card at the designated points. They have a pickup point where you unlock the bike and then once you have finished your destination you can drop it off as the designated point and the hire cost is deducted from your oyster card. As far as i know the scheme only works in Central London. With the river boat service, i don't know much on this as I've never used it before. I do believe you can use your Oyster card to travel on them. I'm not entirely sure on the start or end journey either but i guess there will be stops in central London as the River Thames is the main route for this boat service.
I have only used the Trains, Tube, buses and taxis in London while i was there. In some countries you have to be careful using public transport at night, the same applies here. Generally public transport in UK is fine.
Hope this helps,
Thx
Jaz