Evergreen is a little over an hour from Denver International Airport (DIA), or 45 minutes from downtown Denver. The drive is very scenic and a bit twisty, but not treacherous. If you're flying in from out of town, you have several options for transportation, but renting a car is probably the most economical and convenient. Here is some information on the transportation options available at DIA.
Hotwire has great deals on rental cars. The catch is that you won't know what company you are going to get, but they will guarantee the rate and the size of the car. Last time I checked there were economy cars from $20/day and full size cars from $27/day. SUV's started at $64/day.
American Eagle Limousine, 303-332-7307: $90 (plus gratuity) Airport to Evergreen for Sedan (1-3 people), $115 for SUV(6 people), Van $160 (10 people), $180 Limo (8 people).
Denver Limo Transportation, 303-523-5553: has rates on website: $80 for towncar Airport - Evergreen, $95 for SUV.