If your are looking for a place to plug into the Denver Magic community than the easiest thing to do is to locate a local Friday Night Magic, or FNM. This of course is simple enough to do, just go to the event location on the Wizards website.
Friday Night Magic events are Wizards approved store run events for MT:G players. Generally they have a relatively laid back environment, where people just want to unwind and relax. Most stores of course foster a friendly atmosphere and strive to help new players.
However, the rules are enforced and it is an actual competitive environment. There are prizes, supplied to the store by Wizards, they are awarded both as door prizes (two randomly chosen players who attended will receive the cards) and as place prizes (the two top players receive a card a piece). Also, your performance at FNM will be recorded and reflected on your DCI rankings.
A couple important things to remember are: All Friday Night Magic events are of course held on Friday, however the time can vary from store to store. While most stores have a standard constructed environment, booster draft is also common in some stores. In addition, sometimes you will see two-headed giant and sealed deck events. Some locations also have a small entry fee. Some stores also provide addition prize material to pass out to the winners.
If the first place you try is not a good fit, look around, you will find a group that matches you.
Arbitrary Thought for the Day: Vizzerdrix is a good reason that law enforcement prosecutes drinking and casting. Don't Drink and Cast Spells.