You do not need Jetson Nano specific tutorial for this (assuming you got no Jetson Nano specific issues with getting your webcam working). I suggest learning OpenCV, with it you can do what you want. Here very simple tutorial about color detection: OpenCV and Python Color Detection - PyImageSearch. If you are interested to learn more, try googling “opencv detect color” or “opencv color detection” to get more results, you can try adding “tutorial” keyword if you are interested in tutorials specifically. If objects are always expected to be in the center and will affect sufficiently large area of the sensor, you could just crop and take average color value, and check what predefined range it matches to determine the color.
Depending on your task and goals, you may want to consider machine learning if you find out that simple approach suggested above or something similar to it is not enough to solve your problem. ML can deal with complicated cases when the object of interest is small or is not present at the center of the image sensor so just cropping and taking average color value will not be enough. Also, ML can learn to deal with different lighting conditions. For such a simple task you can use small neural network so it would consume little resources. To use ML or not, it is up to you, and depends on what you want to achieve.