I guess you are talking about a real chessboard (not in a computer game), in which case you will need a camera of course.
It mainly depends on the camera how you can use it in OBS.
A webcam for example connects to the PC using USB and can be captured by OBS right away. (Add a "Video Capture Device" source and select your webcam).
A "normal" camera might need a capture card though. Capture Cards are either external or internal devices for your PC that can capture Video Input. For example the camera would have an HDMI output and the capture card an HDMI input. In OBS you would select the Capture Card (by adding a "Video Capture Device" source) and the capture card would "grab" the incoming video/audio stream from your camera and "put" it into OBS.
Some cameras might have an interface to directly capture them without a capture card, but this will depend on the camera you use.
In OBS you can then add images, text snippets, sponsor logos or whatever you want and then either record everything as a video file to upload it later or directly stream to a service of your liking.