score:3
Since April 2016, the RTD A Line is now in operation. This is a direct rail line from Denver International Airport to downtown Denver (Union Station). See this answer for details.
Union Station is right at the northwest end of the 16th Street Mall. There is a free MallRide shuttle bus running the length of the mall, if you want to get to a different point.
Upvote:3
As @Flimzy pointed out. Google Maps has pretty extensive public transportation information. So you can simply try to get the options from it.
In addition you can look at RTD, which allows you to do the same thing but in the end uses Google Maps for rendering options.
Upvote:3
While Wikivoyage is a good place to check for info like this you can generally find good info on the relevant official airport website. At least I have been able to most times I've tried.
So, here's Denver airports official page. Following the Ground Transportation / Public Transport links gets you to a page about the SkyRide public bus service. From there you have to go to the RTD site and find the SkyRide page, but you can find out that the AF runs from the airport to 16th Street and (if I'm lucky and it doesn't expire) this is a direct link to that schedule.
That may not be the fastest, most regular (it looks like it doesn't run all the way to 16th street that often, so may be better if you get off earlier and change), or cheapest way -- you can follow Karlson's suggestion to compare other routes.
And, once you've done it, you can always update the Wikivoyage page for future visitors ...