FAST responded before I did but that's alright, heh.
The earliest way to access DS mode was via a slot-1 PassMe and a traditional GBA flash cart. The PassMe pulled the authentication information from a legit DS game card inserted into the back and rerouted code execution to slot-2. WifiMe was shortly discovered afterwards and acted as a virtual PassMe using a hacked DS Download Play image. FlashMe then appeared, which was a replacement firmware for the DS which made it so you could boot slot-2 in DS mode automatically (though you needed either a PassMe or Wifime at least once to install it in the first place).
As newer DS units came out, the PassMe stopped working, so the PassMe2 was created as a workaround but it needed to be programmed to work for a specific game and was rather clunky to use. Eventually NoPass devices came out, which were standalone slot-1 carts that didn't require anything else sticking out of the DS to boot to slot-2, and these included things like the Superkey and PassCard 3. At this point in time, the most popular slot-2 device for homebrew only was the GBA Media Player v2, CF version. It allowed for easy DS homebrew loading, and was one of the first (if not first period) to support FAT filesystem access which later evolved into the more universal DLDI architecture with libfat. Prior to having this filesystem access, all game assets were packaged into the *.nds file itself, much like in the GBA era, though you had a 4 MB filesize limit for everything. The earliest versions of NES DS, for instance, required you to package your games into the .nds file keeping in mind that 4 MB limit, and same with SNES DS which meant that you could only play smaller games unless you had a GBA-capable slot-2 device.
Some of the earliest standalone slot-1 carts were the Neoflash ones as FAST mentioned, the DS Link, something with "Ninja" in the name, and only later did you start getting the ones from the major slot-2 manufacturers which are the names that you would recognize today (M3, R4, Supercard, EZ-Flash, Datel, Acekard).
The links FAST6191 posted should be helpful, and you might be able to gleam some information from the various pages at
http://www.pockethea...
S_Flash_Cards as well - this wiki is terribly out of date for DS stuff, but it's got some info about these earliest DS carts that you may find useful.