How does a path become a public right of way?

In legal theory most paths become rights of way because the owner “dedicates” them for public use. In fact very few paths have been formally dedicated, but the law assumes that if the public uses a path uninterrupted for at least 20 years then the owner had intended to dedicate it as a right of way. 

A public path that has been unused for 20 years does not cease to be a public right of way and the legal maxim is “once a highway, always a highway”. 

You can find out more ways paths can become rights of way through this page: https://www.ramblers.org.uk/advice/paths-in-england-and-wales/changes-to-the-path-network/creating-a-right-of-way.aspx