As discussed here - in order to assign a worker to a resource you must be in workshop mode and then approach the person you want to be the worker, speak to them and "command" them:
...then go to the location you want them to work and you'll have the option to assign them to that post.
They'll then walk over from their original position and start working.
The person icon will go red again if you reassign a person who was already assigned to another task, or that person is currently not performing that task (ie: sleeping). Unfortunately, there is no method of seeing an overview of all tasks your settlers are currently assigned to, however you can see what each individual is assigned to if you have visibility of that individual and their assigned task - this picture will show you what I mean:
This settler is only assigned to half of these carrots, another settler is doing the others, so when I target this settler is highlights half of the carrots.