My flight lands at Heathrow (United) at 9:40 and I need to get to St. Pancras for a 14:22 train. What is the fastest way to get there?
Heathrow Express to Paddington followed by the Tube or a taxi to St Pancras is the fastest (less than an hour), BUT the Piccadilly line of the Tube goes straight to St Pancras from Heathrow, in perhaps 75 minutes, which you can probably spare given that you have over 4.5 hours between the flight arrival time and the train departure.
We did the Heathrow Express + Tube transfer in 35 minutes. ( We did not have to wait long for the train!)
There are stairs from the HEX platform at Paddington directly up to the Tube access area which can save time. But I don't know if you will find ticket machines there. We had Oyster cards.
If you want to save money on the Heathrow Express, buy your tickets well in advance.
Agree that the Heathrow Express + Tube (~£24 off peak) or the direct Picadilly line (~£3.10 off peak) will be the fastest. Time of course depends on both the day and the time of day. Tfl for London may show that the Tube may be faster than the Express +Tube.
The easiest would be to take the tube. The Piccadilly line will take you directly from Heathrow to Kings Cross/St Pancras and will be the cheapest way as well. It will take almost an hour. Why pay more for the Heathrow Express and then hassle with transferring to the tube or a cab when the tube will take you there directly and cost you much less money?
The Transport For London Trip Planner is your best friend whenever you're in London.
Also of note - the UK recently added USA to the list of countries whose citizens can use their "E-Gates" at the border control points. This greatly reduces the time required to clear border control.