I pull mine apart and eat the icing first.
The icing has to be completely either on one cookie or the other. If not I lose. 
I’ve heard of dunking them in coffee but I’ve never done that.
Frankly, I’m not a fan of them. I’ll nibble on them if they’re around, but they’re not on my Must Buy shopping list.
I pull two apart make a double stuff and throw away the rest. Dipping in coffee or milk is to die for.
I pull the Oreo apart and eat the half with the icing on it. I break the other half into bits which I throw to my doggies, who love a cookie every now and then.
Double stuf, usually chocolate or the new to-die-for peanut butter creme.
Dipped in milk till slighty smooshy, chomp. NUMS!
I don’t eat my Oreos anymore. 
When I used to, though, I would get several Oreos, pull the icing out of the middles, stack the icing onto one half of the cookie, top this icing tower off with the other cookie half, munch.
Repeat until the bag was empty, then I’d have all these yummy little chocolate cookies to eat up. Yums!
My spousal unit sticks the tines of a fork into the middle so as to hold the cookie in a glass of cold milk till the bubbles stop. Then he snarfs it down.
Me, I just eat them as they are - chomping into their sammichy goodness.
I eat them in a slightly weird way; I let them get stale. Not too stale, mind you, just “out on the counter for a day in humid Illinois” stale. Nothing is better than that.
My friend introduced me to dipping oreos in salsa. Don’t gag, it’s really good!
I eat 'em up whole, shovel-fashion.
But I actually prefer generic ones. The cookie part is usually softer.
(Note: The following applies to any sandwich cookies, not just Oreos)
I just eat 'em normally, like any other cookie.
But when I was a kid, I’d pull them apart, first eat the half without the frosting, and then eat the half with the frosting. I was into Delaying Gratification at a very early age. (It was much later that when I got Carpe-ing the Diem, thanks to the mice that ate the candy bar I was saving for later.)
I dip half in milk till softened, eat soggy portion then repeat. Two for the price of one!
Those Double Stuft ones are kinda gross, IMO.
Dip 'em in milk until they’re soggy, then chow down. Mmmmm…nothing else like it on earth.
And the peanutbutter ones are to DIE for!
I tend not to eat Oreos. I prefer duplex cremes. Which leads to the fun of “Which color gets the filling?”
Grasp cookie. Twist. Does the creme stick to the chocolate side or the vanilla side? Take notes!
[post=6347952]Here’s how I eat them[/post]
Note: the key is to let them get soft, almost but not quite to the point of falling apart and turning into sludge at the bottom.
I used to eat the icing first, because it is gross, and it is good to get the eating-the-icing part out of the way. Then I savored the delicious chocolately goodness of the halves, dipping them in milk if I have any hand.
Now that I’m on a diet, I don’t eat them at all. There are much more satisfying ways to consume an equivalent amount of calories. Oreos also have an ungodly 2.5 grams of trans fat per 3-cookie serving. (3 Oreos are a serving? Who the fuck eats three Oreos?)
I think I have eaten a grand total of 10 Oreos in my entire life. I just don’t like them much.
On the occasions I have, I’ve eaten the frosting and thrown away the cookie. Sorry.
Sounds like if Podkayne and Anaamika ever crave Oreos they should go in halvsies.
I dip them in milk, until the black part is completely smooshy and carefully eat that away, being careful not to touch the icing. Then (assuming I was successful in not hurting the icing) I eat that all at once. If I accidentally do get the icing, then I just eat it with the smooshy black part.
Another fun thing to do is when the package is almost empty, and you have mostly broken pieces and crumbs is to take the bag, pour the contents into a bowl, pour milk on, and eat it like cereal.
I like mine ground up and mixed with butter. You flatten that out in the bottom of a springform pan and add cheesecake mixture over it. Usually the cheesecake mixture has Reeses Pieces and Smarties in it. It is the only way to eat Oreos.