Editor - length of term

How can I find out how long a particular editor has been moderating his/her category?

If you are an editor, you can find out in that editor's request logs, which contains the details (and dates) of all permission changes.

If you are not an editor, quite simply you cant ... not without asking them.

As a non-editor you can use for example http://web.archive.org/web/*/http://dmoz.org/Regional/ to see how the listed editor has changed through the years for the Regional/ cat. And hence see how long an editor has been editing a particular cat.

However do note that an editor listed in a cat can edit all the subcats of it. Also there are editall+ editors who can edit anywhere.

If you're an editor there are much easier ways to ascertain the above.