Easiest way is to take a cab but it'll cost you. Last time I did Heathrow to the East End of London, it was about 60 pounds. Cheapest but more time consuming is the Coach Service. Just make sure it's going counter-clockwise around the M25 or you'll be on it for an eternity.
Personally I'd take the Victoria Express from Gatwick to Victoria Train Station. Get on the Picadilly line tube and stay on it until the end at Heathrow. Then catch a cab to the Mariott or a van, if they provide one. Sorry I can't remember how to get on the Picadilly line from Victoria, it's been a while since I lived there.