Update, September 2016:
This guide is a mess, but I’m leaving it here for historical reasons.
Prerequisites. Obviously, you need a Nintendo DS capable of running homebrew (via a flashcart + SD card; the flashcart must support .nds files) and a computer running Windows, Linux or OSX.
Get the software. You will need the following (skip down for an alternative resource):
* Mini vMac for DS (get it from here)
* the “normal” Mini vMac (get it from the official site; under Linux, run the Windows version with Wine)
* blank disks (archive here)
* System 6.0.8 (get it from Apple: disk 1, disk 2)
* either The Unarchiver (if you’re on a Mac), an older version of StuffIt Expander (5.5 or 7.0 should suffice, see here) or some other software that can extract StuffIt files, if you somehow manage to find it
* vMac.ROM (probably illegal to distribute, but grab it from here anyway)
Extract. First, extract Mini vMac DS (you should put the “vmac” folder on your SD card’s root and extract the 2MB binary to it; the ui_gfx folder should also be there). Then, extract the “normal” Mini vMac to a folder on your computer, along with System 6.0.8 (install Aladdin to extract it; you want two files: System Startup and System Additions), one of the blank disks (choose a size from the .zip and extract the .dsk) and vMac.ROM (capitalisation is most likely important, so rename it if necessary).
Install. Run Mini vMac (on your computer), open the System Startup disk and the blank one (you should get prompted to initialize it; if not, single-click it and go to Special -> Erase Disk), run the Installer (it’s on the System Startup disk) and follow the instructions. Then safely shutdown the virtual machine (Special -> Shut down) and proceed to the next step.
Copy the files. Rename the blank disk’s file to “disk0.dsk”, then copy both it and vMac.ROM to the “vmac” folder on the SD card.
Done! Now just use your flashcart’s launcher to run MinivMacDS.nds.
If you get any “this disk requires minor repairs” error, don’t hit OK, it won’t work. Shut the DS down, run the “normal” Mini vMac again, open the disk image and repair using that. And don’t forget to shut down safely!
I haven’t tried loading any software on it. If you do intend to do that, you’ll probably have to use the computer to copy software over to the disk. And by the way, you should be able to load additional .dsk files by renaming them disk1.dsk, disk2.dsk, etc. (up to disk4) and copying them to the SD card root.