From Heathrow (west) or Gatwick (south) the simplest transfer is the train. The Heathrow Express gets you into Paddington in West London in 15 minutes and the Gatwick Express into Victoria (South London) in 30 minutes. Both run a service every 15 minutes.
You can get the tube (underground railway) from LHR, which is better if you are travelling on into Central London, but it doesn't reach out to LGW.
Taxis are relatively expensive and get stuck in traffic. Buses only slightly better unless you are travelling to places other than London.
If you are anything more than unimportant, your company would send a driver to meet you in the airport concourse - either one of their own, or for a smaller company, a minicab (private hire).
HTH
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