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 usually is to take HW 9 out of Steamboat south 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.