Denver International Airport (DIA) is a 3 1/2 drive from Routt County depending on road and weather conditions. The locals best (fastest) route is to take highway 40 East, until Kremmling, turn right onto Highway 9 at Kremmling toward Silverthorne. At Silverthorne head East on I-70 to Denver. Continue on I-70 east through Denver taking Pena Blvd to DIA.
If you have time for a more scenic route you might take HW 40 through Hot Sulpher Springs. This route is approximately 30 minutes longer. Another alternate route, though longer, is to take HW 131 south out of Steamboat to I-70 then east to Denver.
Below is a link to the DIA website, where you can find out flight, parking, weather and general information.