I just upgraded the RAM on my Mac Mini and it has made a big difference to performance so I figured I would share some tips on this type of upgrade. (So many people share helpful information on the Web I've been feeling guilty that I have not done more sharing myself, so hopefully this will help make amends.)
Ironically enough, my first tip is to watch someone else's video of how to do a Mac Mini RAM and hard drive upgrade (it may make sense to do both upgrades at once--you have to take the thing apart in both cases, pun intended--but you don't have to do both, the video is helpful either way). This is the best video I saw during a fairly extensive review of what is out there. You can find it here on Vimeo.
I suggest you watch the video and, if you still feel like going forward with an upgrade, consider the tips I have written up here before you start (unfortunately, hardware can be more difficult to work with than it appears in such videos).
My second tip comes after you separate the outer case from the innards: Get a magnetic to use with your screwdriver. I use a magnetic hook. You attach the magnet to the metal shaft of the screwdriver so it will pull the screw out of the hole when I lift the screwdriver (helps to keep screws getting lost inside the case or on the floor). (These magnetic hooks are Neodymium and coated with soft plastic so they don't scratch. They have a holding power of about 9 pounds and I use them for hanging up key rings. You can order them here.)
Third tip is to mark the corner that requires a screw that is longer than the other three. I marked this on the optical drive cover with a thin Sharpie.
My fourth tip concerns removal of the 2-wire power connector as shown in the video. Do this very carefully, prying the black connector out of the socket. do NOT pull on the wires as they may be brittle (I ended up breaking one and fixing it was a pain). I think the key to getting this one right is using good lighting and possibly a magnifying glass.
Next up is the pulling the drive unit out of the innards, so to speak. You need to do this with care because there is a ribbon cable that wires the drive unit to the innards and it must not be strained or disconnected.
Complicating matters is an edge connector that must be pulled out, which means you do need some force to get the two parts apart. Then you will need to support the drive unit while you perform your RAM upgrade. The video glosses over this but the solution is very simple, just place the outer case under the drive unit.
Here you can see the drive unit on the case with the innards exposed ready to proceed. But first, I suggest you carefully place the whole thing on a tray of some kind and take it some place you can blow off the dust with an air can (or suck off the dust if you have a computer vacuum).
What looks like mold growing on the unit in the picture is dust. The fan unit is likely to be full of dust as well. Blow this out carefully, in a well-ventilated area. No point opening the case without performing this bit of preventive maintenance (Mac Minis are known for being super quiet but mine had started to make some noise--this cleanup returned it to quiet mode).
The video has good instructions on changing the RAM. My machine had two 512 megabyte memory cards and I simply replaced the top one with a 2 gigabyte card. This gives me 2.5 gigabytes total and seems to make the Mac Mini work a lot better (programs load faster than I'm not getting so many delays when running multiple programs at once).
Final tips concern re-assembly. Be careful that you thread the BlueTooth antenna cable the right way or it could get pinched. Also make sure that the wires crossing the ribbon cable do so neatly, within the fold of the cable. Finally, as recommended in the video, test things before you put the outer case back on. This has been a habit of mine from my earliest days making PCs out of cloned motherboards. The cover doesn't go on until everything checks out, otherwise you jinx things!
Well, that about does it. One final tip is to make sure you have access to the video while doing this. I downloaded it to my Windows laptop so I could watch it while the Mac was in pieces. Good luck with your upgrade!