The starting point for handling any potentially hazardous material is the Safety Data Sheet. This is a document (made to a worldwide standard) that details how a material should be handled. The SDS is prepared by the material's manufacturer.
Rocket propellants can be hazardous, and finding out how hazardous exactly isn't the safest job in the world. The book Ignition! gives a good idea of how that worked in the early days of space travel: by trial and error. Small amounts of a new propellant were made and then experimented with: they were exposed to various materials and temperatures, they tried to measure how easy or difficult it would be to ignite etc. Each error was punctuated by an explosion...
The government usually has regulations on handling hazardous materials. In the USA, these are created by the Occupational Safety and Health Administration, OSHA.
In some cases, a company has to find out for itself how a propellant works. For example, SpaceX uses supercooled liquid oxygen, which behaves differently to 'normal' liquid oxygen (which is used at its boiling point). They found that out the hard way when a rocket exploded during a prelaunch test for the AMOS-6 mission: the colder-than-usual oxygen in contact with a helium storage vessel led to the explosion.
Organizations like NASA sometimes publish their experiences with a propellant as a reference for others. Commercial companies are less likely to do that.