Here is the RTD schedule and stops for rides to and from DIA, but you might want to use a shuttle service. It will drop you right at your airline, and pick up from a designated spot after your trip.
It depends on what else you are doing during your time here. If you are just planning on staying downtown then you can take an airport shuttle or a bus. The public transportation downtown is not bad at all, however if you are planning on going anywhere outside of downtown then the options are more limited and I would recommend renting a car.
Super Shuttle, I have used it many times from DIA to downtown Denver hotels. Roundtrip should be $44 plus taxes and maybe a tip. Its going to be far nicer, easier, and faster than public transit.