Well, if you are serious about getting to the Brecon Mountain Railway, your easiest way is to contact the WHFR subsidiary Ffestiniog Travel by way of the website www.festrail.co.uk who will happily arrange the whole trip for you (normal commercial discounts are one of the ways we raise money), Ffestiniog travel has a turnover close to one and a half million pounds ($2m) a year.
If you really want to book it the hard way you would fly from Denver to London Heathrow where you would catch the Heathrow express to Brunel's great Paddington station in central London. Changing trains at Paddington you would take the 125mph express to Wales' capital city of Cardiff where you would change onto a Valleys train to Merthyr Tydful, site of the first ever successful use of a steam locomotive to haul a train. Then I'm afraid you would need a cab for the four or five miles to the Brecon Mountain Railway. You can make discounted bookings, and get train times, from Thetrainline.com if you don't want to use Ffestiniog Travel.
Bob Gartside