If you're flying into DEN, take the take the A train to Union Station. From there, the Sheraton is a 25 minute walk. Trains run every 15 minutes.
From Union Station, you can also hop on the 16th Street free mall ride which runs every 4-6 minutes and get off on 16th Street Mall & Tremont Pl. The ride runs from 5 AM to 1:30 AM.