On June 21, I'll post a question collection post on Meta, so that the community can post questions they'd like to see the candidates answer.
Starting on June 28, users can nominate themselves. The top questions collected on the previous week will be compiled into a second Meta post, so that potential moderators can answer them.
On July 5, if there are four or more candidates, we'll run an election. If not, we'll extend the nomination period for one more week. If at the end of this extension period there are still not four or more candidates, I'll simply appoint the candidates who've nominated (and aren't already pro-tem mods) and we'll default to considering this a "pro-tem election" just to try to bring the total number of moderators on the site up to 3 (for full details of the process, see the announcement on Meta Stack Exchange). (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 July 13 (or on the 20th, if we need to extend the nomination period and only get 4 or more candidates then).
If you have any questions about the process, please stick them in an answer here.