Step 2: Cities and Areas

In common conversation, "Denver" could refer to many things.
The City of Denver,
The County of Denver,
The Denver Metro Area,
The Denver Omelet,
John Denver....
...I can't help you if you're trying to drive a Denver omelet,and I don't think John gets around much anymore...

In reality, there are 20 or so adjacent cities that make up the "Denver Metro Area", which is what most people use to refer to, um, the denver metro area.
A nifty  map with all the cities is below, but I'll outline the most common ones:

Downtown: Slang for the City of Denver, which encompasses all the big skyscrapers and sports teams; the center of all that is Colorado
Lakewood: The west side of town; the biggest city gets the naming convention. Populous.
Aurora: Conversely, the east side of town. Shady folk here.
Wheat Ridge/Arvada: Northwest Denver, mostly residential, except when it's not.
Littleton: Southwest Denver, suburbs and Lockheed Martin MI complex; stay away unless you have a missile to sell.
The Tech Center: Included: Englewood, Centennial, and Highlands Ranch; Straight south down I-25, headquarters and branches of seemingly every white collar corporation ever, and the mother source of all of Denver's rush hour traffic. Seriously.
Westminster: Like Arvada North, except, well, it's Arvada North.

Also notable:
Golden and Morrison: Make up the far west and southwest edges of The DMA, very nice little towns, except for the foul monstrosity of the Coors plant. (Red Rocks is in Morrison, though, so it balances out)
Boulder: Far far away up to the Northwest, everyone should know where Boulder is so they can avoid it like the plague, unless it's April 20th.
Castle Rock: Surprisingly Stephen King free, CR is in between Denver and Colorado Springs, and has a rock that is apparently heavily fortified. Detour around if unarmed.

If you're new in town, you'll probably have experience with the airport, which is currently Denver International (there's been like twenty airports in the last 50 years, whatever.)
DIA is kind of interesting, it sits 40 miles northeast of downtown, but the city bought up all the land along I70 and now the city and county of Denver extends wayy on up, for some reason.  DIA is actually pretty nice, considering it sits in the middle of a cornfield and is shaped like a swastika...