Summarised here for reference: subject to update if the maintainers have a better idea.
Holes: these recently occurring natural (or unnatural) phenomena allow some transit between the worlds; however, since you can't be sure where you'll end up in the world you're jumping to, and since you don't know how long the Hole will remain open, they are a very risky method of transit. The Holes should not be relied upon for regular trips, and in fact, players are encouraged to deposit themselves in awkward situations.
It is possible that Urahara, Twelfth Division, and others may come up with some way of manipulating/investigating Holes in play. The mods will take this as it comes.
A Hole looks like a rip in space; you can see what is on the other side (Hueco Mundo, Earth, or Soul Society) but not precisely where. By now, most of Soul Society is aware of the Holes, and a general order has been issued to avoid them. In Hueco Mundo, Arrankar (and other Hollows) have been ordered to leave them alone for the moment. Nobody's got round to telling the humans on Earth yet.
General travel: any Captain or Vice-Captain from Soul Society can reach Earth; however, if they are caught there without permission, they will be punished. Anyone from Hueco Mundo can reach Earth; again, however, if caught without permission, they will be punished. People on Earth can reach Soul Society or Hueco Mundo by going with an inhabitant, through an Urahara-gate, or by using one of the Holes (though they are requested to keep this within plausible limits). People in Soul Society or Hueco Mundo can reach Hueco Mundo or Soul Society via a Hole (though again, please keep this within plausible limits) or via Special Tech or Kidou which will need to be mod-cleared.
We are attempting to make this straightforward, with a reasonable amount of handwaving, to simplify things. However, if characters do keep on popping backwards and forwards without actually having been sent on a mission, they will have to answer to Higher Authority.
Also, it is assumed that any Vice-Captain or Captain on a formal mission to the mortal world will have received a Limiter on their powers which will reduce them to 20% of their normal level. Formal contact and authorisation from Soul Society is needed to use full powers.