The "election" is merely a way to help Jeff choose the next moderator(s). He did not publish the results last time, is not likely to this time, and is not bound by the results. At best this process is used to make sure that 1) the candidates want to do the work and 2) the users of SO like them well enough to put up with them (ie, give Jeff less grief)
In the prior election, your questions were answered as follows:
Say the process is as simple as people voting in a CW thread (as was the case with the nominations)...
The voting was done on a custom page on stackoverflow which allowed each user with 200 or more rep to vote once. It was not done in a typical question/answer format.
What users are eligible? (does a member have to have had an account for a minimum period of time? what about a minimum rep, question/answer ratio, upvote/downvotes (received) ratio?
Users with 7k+ rep are eligible to be candidates, assuming they are nominated, Users with 200+ rep are eligible to vote.
What is preventing users from creating duplicate accounts so as to cast multiple votes?
Nothing that was visible during the voting period last time.
How are complaints to be resolved? Complaints could come from the candidates, as well as from the voters. Unbiased people must be available to offer assistance.
Candidates were free to refuse their nomination during the voting process by emailing email@example.com. Users that had voted for them were given their vote back, and notified next time they visited SO that they still had a vote.
Given that this was not a democratic process, no other measures were in place, but right now you can either email the team, or bring issues up on meta.
How long will the voting be open for, and will it accomodate users equally in all timezones?
Voting lasted a week.
How long will nominations be closed before voting begins?
It was more than a week between nominations and voting last time. A lot more.
I'm guessing it'll be 6-8 weeks.
How will voters be notified that there is an election?
The notification bar (ie, "You received 2 answers and three comments") that appears sometimes when you visit SO will show up for every eligible voter when they visit SO during the voting period. It will continue to appear until they vote, badgering them, day in, and day out. It will appear in their dreams, and haunt them at their workstation. There will be no escape, no respite.
No doubt some will go mad.
But it's for the good of the community, so sacrifice must be made.
May a user vote for (and/or against) more than one candidate?
No. One vote per user.
What process will be used if I wish to retract a vote before the polls close?
You may not. Once submitted your vote cannot be recalled, except in the case of your chosen candidate leaving the race, or if you make a mistake you may attempt emailing the team and pleading your case.
Are candidates allowed to post a statement regarding their candidacy, are there any restrictions as to what they can use in their statement, will this be in a post or may they send these statements to all users?
IIRC, in the voting page candidate names linked to their user page. They were encouraged to change their user page message to whatever they felt would represent their candidacy.
Are bribes and/or bounties permitted on behalf of the candidates?
Nothing that I saw was done to encourage or discourage any activities that occurred outside SO.
May users pose questions to the candidates? Will this be a free-form discussion thread, or should questions be submitted in advance to all candidates and answers prepared?
I think there was a question with an answer for each candidate, and they did respond to comments there. I don't recall exactly though.