By default, homebrew that utilizes the DLDI framework will probably work on a specific device (the one the author uses) but can be patched to work with any device listed on the devices page.
So, after downloading the DLDI enabled homebrew, you need to patch the .nds or .ds.gba depending on what you are using.
First you need to obtain a patcher for your device. Start by going to the tools page and download your prefered tool.
Next, you need to download the DLDI driver patch for your device. So go to the devices page and click on your device and download the .dldi file.
Follow the instructions for your prefered tool. Once you have patched the .nds or .gba file, you can copy it to your memory card and run it from your DS.
If you have multiple devices, it may be a good idea to rename the patched files something like this: