How does SE moderation work during the private beta? Is it just general network moderators, are users assigned, or is there a vote?
There are no moderators in the community other than the SE staffers, at the moment.
Here's how and when Stack Exchange chooses the pro-tempore moderators for a new site, quoting from this blog post:
About a week into the public beta, we will seek out members who are deeply engaged in the community’s development; members who:
Have a reasonably high reputation score to indicate active, consistent participation.
Show an interest in their meta’s community-building activities.
Lead by example, showing patience and respect for their fellow community members in everything they write.
Exhibit those intangible traits discussed in A Theory of Moderation.
For the time being, we are relying on SE staffers to take care of issues we can't take care of ourselves (responding to flags, for example).