Use a Nintendo DS capture card or modded hardware
Install the capture software provided by the capture card maker
Connect the DS to the PC with the required USB cable
Launch the capture software on the PC
Open the DS game on the console
Adjust video and audio settings in the software
Use OBS Studio if you want to record or stream the capture window
Add the capture software window as a source in OBS
Set the correct resolution and frame rate in OBS
Start streaming from OBS to your chosen platform
If using a DS emulator, run the game in the emulator on PC
Capture the emulator window with OBS or similar software
Use a stable internet connection for live streaming