Summary: Cardano Stack Exchange will begin the nomination stage for a special election on May 31 to bring in your three inaugural pro-tem moderators — congratulations on making it out of private Beta!
For full details of the process, see the announcement on Meta Stack Exchange. The timeline:
Starting on May 31, users can nominate themselves. Users can also ask questions on meta for potential moderators to answer. (Use the discussion and election tags.)
On June 7, 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. (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 15 (or on the 22nd, 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.