By Train:
From London to Eltham: Trains run from Charing Cross, Waterloo East, London Bridge, Cannon Street and Victoria. You need the ones that say "via Bexleyheath". There are 2 stations that you can use - Eltham and Falconwood, depending on which end of Eltham you want.
From London to Mottingham and New Eltham: Trains run from Charing Cross, Waterloo East, London Bridge, Cannon Street and Victoria. You need the ones that say "via Sidcup".
By Plane:
From Heathrow Airport: The easiest way is to arrange for a cab to pick you up - have a look on the Shops & Services page to find a local one.
The cheapest way is by train - Heathrow Underground station runs trains to Charing Cross and Victoria (Piccadilly line and then District or Circle to Victoria or Embankment for Charing Cross. We usually change at Barons Court as there are no steps to navigate), the Heathrow Express runs to Paddington Station where you can get get the District & Circle underground line to Victoria or Embankment (for Charing Cross).
From Gatwick Airport: Again, the easiest way is to arrange for a cab to pick you up - have a look on the Business in SE9 page to find a local one.
The cheapest way is by train - they go from Gatwick Station directly to London Bridge Station.
From City Airport: Again, the easiest way is to arrange for a cab to pick you up - have a look on the Shops & Services page to find a local one.
The cheapest way to get to/from London City Airport is to use London City Airport DLR station. The service running from London City Airport has connections with Lewisham and from there you can change to the Mainline Station for travel to Eltham, Mottingham or New Eltham stations.
Alternatively, you can take the DLR extension to Woolwich Arsenal and catch a bus or taxi from there.
From Stansted Airport: The easiest way I know is by car, via the M11 and M25. The train line is into Liverpool Street Station.
By Road:
The A2, A20 and M25 all run close by, or through Eltham, Mottingham and New Eltham.