Hi - thanks for asking!
We have actually submitted a paper to the Astrophysical Journal late last year, and received the peer-reviewers feedback. I'm putting the finishing touches on the second submission right now (it's open in another window on my computer right now), and we should have it resubmitted within the week.
The way peer review works, is that you submit your manuscript, a reviewer (another scientist in your field) digs through it, looking for errors and double-checking your work. Then he/she sends back a recommendation and several comments. For this paper, the reviewer recommended it for publication once a major issue and several minor issues are addressed (this is considered a very positive review). Currently, I have very nearly finished addressing the issues, then I'll send it off to the co-authors, who will provide additional feedback. Then it gets sent back to the reviewer, who will hopefully approve it for publication.
Basically, papers go back-and-forth between authors and a reviewer until everyone is satisfied (if one side cannot be satisfied, the are other options). Then it goes to the copy-editors, who create a proof for us to approve, then to publication!
This current paper, which uses results from Milkyway@home, could realistically be published in February. We'll keep you informed!