Gatwick
Simply jump on the 30 minute train from Gatwick to Clapham Junction. Then change onto the Overground, direct to Kensington (Olympia).
Heathrow
The Piccadilly line goes straight to Heathrow. Olympia London is only a 5 minute bus ride, or 9 minute walk away. Alternatively, take the Heathrow Express train to Paddington. Then travel to Hammersmith, using the Circle or Hammersmith & City line.
Stansted
The Stansted Express goes to Liverpool Street. Then change onto the Central line for Shepherd's Bush, and take the Overground one stop to Kensington (Olympia).
City Airport
Take the Docklands Light Railway (DLR) to Bank. Change onto the Central line for Shepherd's Bush, and take the Overground one stop to Kensington (Olympia).
Luton Airport
Take a train from Luton Airport to St Pancras. Change onto the Victoria line for Oxford Circus. Then change onto the Central line for Shepherd's Bush, and take the Overground one stop to Kensington (Olympia).