make it shared across my LAN with others so that they can pull a copy on their own PC and work on it, and push their changes to the project, and thus make it available to all devs concerned.
You want some sort of version control system to avoid the special hell that is conflicting edits.
What is the best way/tool available to share such a project freely on a LAN?
There are more than a few systems out there, depending on your requirements...
What tools would be required for each user to get access to be able to pull/push a copy from their PC using VS 2015?
Off the top of my head, Visual Studio integrates with Git and Subversion; there are also VS plugins for other source control systems.