What are PATH and other environment variables, and how can I set or use them?

Questions about

• setting environment variables


• the PATH

are very common here, and in most cases the answers are very similar to each other. In the future it would be nice to have a good Q/A for this.

So the question is: What are environment variables, like the executable PATH, and how can I change and use them on major operating systems?

A good answer would include a simple explanation of what environment variables and especially PATH mean to the OS, as well as simple guidelines on how to set and read them accordingly.