Getting to Roatan is the easiest part of the trip, with short non-stop flights by major US carriers from Miami, Atlanta, Houston and Dallas. All of these flights are less than 3 hours and will land you on the islands' International Airport located on the South-Western side of Roatan.
American Airlines - Miami and Dallas
United Airlines - Houston
Delta Airlines - Atlanta
There are also plenty of other flight options connecting in nearby airports such as El Salvador served by Avianca, Tegucigalpa and San Pedro Sula both served by Avianca, United and American. There are also smaller local airlines that will take you from Tegucigalpa and San Pedro Sula to Roatan, and there is also ferry service from La Ceiba in mainland Honduras.