These instructions and a little common sense can also be used to replace the lower hard drive in the server version of the Mac Mini. Luckily that was the drive that had failed in my case. Replacing the upper drive looks like a tougher proposition.
Instructions worked like a charm on my 24" 2134 (taking into account reader's contributions for Step 9). Someone suggested covering the LCD with clingfilm ("Saranwrap") and this is an awesome idea. I was able to have a helper hold the panel while I worked on the hard drive and got no dust or fingerprints on it at all.
A tip if you are replacing the stock hard drive with an SSD: install the SSD onto its carrier so it'll fit in the space left by the hard drive before starting so your helper doesn't have the opportunity to be sarcastic while waiting for you to do it in the middle of the build :-)