Two things, first is to transfer what was said in that other thread someone linked to;

Basically, a person dies in the mortal world and their spirit crosses over when Shinigami do the Soul Burial thing or when they turn to Hollows and are subsequently destroyed by a Zanpaktou.

When they cross, they appear in Roukongai as they appeared in the mortal world and live off water since they dont' get hungry since they have no energy to sustain. Some sho so have spiritual power usually become Shinigami and so on and so forth.

When someone dies in Soul Society, either form sickness or being killed, their spirit crosses back over to the Mortal world and begins a new life with presumeably no memory of their previous two (or more) incarnations.

People age normally in Soul Society except at apparently a much slower rate. Though I'd like to bring up the Dimentional Time difference Yourichi blabbers on about between the Mortal world and Soul Society. I'm looking for the episode again so I'll elaborate more when I do.