This is a known thing that if you wish to run programs compatible on some other platforms on computer, you need to do that by using emulators. So, we would be talking of free Nintendo Emulators which would let you play Nintendo DS games on computer.
All the below listed emulators are completely free and you can easily get Nintendo DS ROMS for the games that you can use on your computer.
3 Free Nintendo Emulators To Play Nintendo DS Games On Computer
DeSmuME
All you to need to do is download the DeSmuME files and then unzip all the downloaded content to a location where you want. Then the .exe file is the one which would actually let you play DS ROMS on your computer.
And in order to play any particular DS ROM, you need to click on the Open button and then select the .nds file of the ROM contents that you have downloaded and it will let you play that DS Game on your computer.
DGEmu
Look for this emulator and download the zip file on your computer. Unzip its contents, and launch the emulator. And click on the File option and then on the Open button. Choose the nds file that you want to run, and this emulator would help you by playing that Nintendo DS Game on your computer.
No$gba
Its latest version is a paid one, but you can anyways manage with its free version, so just download it on your computer. This is similar to all other Nintendo Emulators. Just launch it and open the DS ROMS of the games in order to play them on those emulators.
You can surely use any emulator with any DS ROM. But if you are looking for the free DS ROMS, then you can look out at PDROMs and Homebrew ROMs. Let us know if these emulators work for you to play Nintendo DS Games on computer.