Help understanding many to many relationships.

I need to establish a relationship between 3(maybe more) tables but I'm getting lost trying to figure out how this should work. I have a form that tracks product updates but to keep the form simple i'd like to automatically pull some other data using relationships.

My form collects 3 pieces of info about the product updates. The UPDATE ID, DESCRIPTION, and AREAS AFFECTED. Update ID is usually a 4 digit number, the description is just a general description of what changed and the areas affected is a group of check boxes and their data is passed as an array.

I want to have this setup so that I can pull in a list of people who work in each affected area. So far i have a table with all available areas so each area has an ID. I also have a table for employees and each one has an area_id and a table for the basic info from the form.

I don't understand how to go from an array of affected areas stored in my table to anything.