From my experience (E2/C2), you prepare a dream sheet as you start the FRS. Shortly thereafter, your class will be told how many spots exist in various locations. When I chose, they left us alone in a classroom and we tried to settle it on our own as a class. In cases where classes couldn't sort it out amongst themselves (and it could get pretty ugly at times) they reverted back to advanced grades in order to assign who picked first, second, etc. We did it the first week of the FRS (since that was the point at which you had to pick E2 or C-2 in order to continue ground school) I imagine that each community may handle it differently though.
If you are interested in one of the Japan squadrons, there typically aren't too many guys/gals jumping at the chance so you may not have too much competition for that slot (if one is available). One additional caveat...If you end up Jet or E2/C2 and want to go to Japan, you will need to meet a slightly higher Carrier Qualification standard during FRS CQ. Japan is considered permanently forward deployed and replacement pilots headed there (or meeting any other squadron that is deployed) have higher CQ GPA and boarding rate requirements during FRS CQ and will complete more traps than CONUS-bound RPs. I don't say this to confuse or scare you, but just keep in mind that there is more to the selection process in that specific case than the standard "desires vs needs of the Navy" issue. There have been pilots who thought they had their Japan slot all locked up and then didn't do well enough at the boat; and likewise those who thought they were staying CONUS, only to find out that they were getting additional traps in order to meet an overseas billet requirement.
Most communities look at an overseas (particularly Japan) tour as a plus in your career, and from my experience they tend to get hooked-up when obtaining followon orders for taking the "hard-fill" billet.