We will be arriving at Heathrow Airport and then need to get over to the Eurostar at St. Pancras station. Any suggestions on the easiest and quickest way to accomplish that trip would be appreciated.
Note that you must check in on the London-Paris Eurostar train 30 minutes before departure. The tube from Heathrow to Kings Cross will take about 1.25hrs. Then, you have the short 1-block walk into St. Pancras. I would suggest reserving 2hrs from the time you begin your journey to St. Pancras from Heathrow to when you get checked-in at St. Pancras.
Quickest an easiest, but not cheapest,mould probably Heathrow Express to Paddington and taxi from there to St. P.
Wouldn't an onward flight connection at LHR be easier for you?
Easiest is to take the Piccadilly Line from Heathrow to Kings Cross/St Pancras. Taking the Heathrow Express/Connect will be expensive, involve a change and probably work out not much quicker. But as Marco asks, as you are already at Heathrow why not fly?
According to various London transport websites I checked, the Piccidilly line is cheapest and maybe easiest (but a long walk involved at the end) but it is not nearly as fast as Heathrow Express + tube from Paddington. About 30 minutes difference (44 min. vs. 75 including walk time). Heathrow Esxpress will definitely cost more. Someone on Fodors suggests car service form the airport to St. Pancras for about 29 euro, but I didn't check the date that was posted. May be an old price.
Heathrow Express to Paddington Station; then taxi (follow the marks on the floor to the taxi stand) to St. Pancras Station. The cabbie can take you directly to the closest entrance for the Eurostar if you tell him/her that is where you are going. Easiest and quickest may be some sort of car service.
"...According to various London transport websites I checked, the Piccidilly line is cheapest and maybe easiest (but a long walk involved at the end) but it is not nearly as fast as Heathrow Express + tube from Paddington..." The websites don't take into account the time it takes to wait in line to purchase tube ticket once you arrive at Paddington after the Heathrow Express. The Picadilly all the way from Heathrow to the chunnel train station at Kings Kross/St Pancras is the fastest, cheapest, and easiest way to travel between the two points.