DIA has pretty good information on its site. Here is page on shared ride services (you can bounce around to other transportation pages from there):
http://www.flydenver.com/parking_tra...it/shared-vans
I haven't looked lately, but in the past Groupon, Amazon Local, and sometimes AAA Member Deals have had airport limo offers.
In general, I would say there is nothing terribly different from other airports which are a bit out of town and not served by subway or light rail: Taxi and Limos will likely be fastest and most expensive, then shared ride services (Supershuttle, etc.), then the bus service. Maybe also check out how much to rent a car for one day to drive out from the airport, drive around some, then return the car to a downtown rental location near your hotel. I am not aware of any downtown hotels having a free airport shuttle, but others may be.