There are several airports in and around London, all of which are convenient. The closest (and largest) airport is Heathrow, but there are airports just North (London Luton, Stansted) and South (Gatwick), as well as in (City airport) the city.
For those travelling from a European country, is also possible to take a Eurostar train which stops in King Cross St Pancrass.
Inside London the best mode of travel is using the London Underground. The cheapest way of travelling is to use your contractless card or purchase an Oyster card. For late night travel, you can take a Black or Uber cab (the latter being significantly cheaper).