I would say the best way is to take the Heathrow Express. I think that is what it is called. It is a bus that takes you directly there. I believe it took 30 minutes. I think it cost $10. Of course I hadn't worked out any of the details when I took it and my flight from Dublin to Gatwick was delayed and only had 1h30m to get from Gatwick to Heathrow to fly home. I was really worried but I just asked someone at the info desk and they told me to take that and I made my flight back to the US alright.

Hope this helps, Tiffany