When I bought my Mac mini a few months ago, I picked it up at my local Apple Store rather than ordering it directly from the company. Because of this, it came with the default 4GB of RAM onboard rather than one of the larger amounts the computer supports. There are probably plenty of mini buyers in the same boat, so join me as I upgrade my mini from a pedestrian 4GB of memory all the way to the computer's max of 16GB.
Start by turning it off (obviously), yanking all the cords (obviously) and flipping the computer over (hopefully obviously).
Apple has made upgrading the newer minis much easier than it was with past models. Simply rotate the black portion of the case counter-clockwise so that it clicks open.
Remove the black cover and try not to drool at how gorgeous the mini's guts are. You can see the memory modules in place on the right side of the interior.
Gently bending the clips on either side of each module will release the memory and allow each unit to be removed. Don't get too aggressive here, the clips might seem "stuck," but don't wrench on them or you'll end up breaking them. Be firm, yet gentle, and they'll eventually bend.
Slide the new memory modules in place and push them down gently. The clips will snap into place once you push the modules down.
Ta-da! You're almost done. Re-attach the black cover, rotate it clockwise to lock it into place and set your mini up as you did before. Enjoy your speed boost!