Summary: Chess Stack Exchange will begin the nomination stage for a special election on June 3 to bring in two more moderators.
For full details of the process, see the announcement on Meta Stack Exchange. The timeline:
Starting on June 3, users can nominate themselves. Users can also ask questions on meta for potential moderators to answer. (Use the discussion and election tags.)
On June 10, if there are three or more candidates, we'll run an election. If not, I'll simply appoint the candidates. (There's a small chance we'll need to remove a nomination, but I doubt that will come up.)
If there is an election, I'll announce the results on meta on June 18.
(Note for current moderators: there's no need to nominate yourself even though you'll likely get an email saying you should. The system assumes the first election is a graduation election, which would mean moderators would need to be re-elected. This isn't that sort of election.)
If you have any questions about the process, please stick them in an answer here.