Phasing causes permanents to enter and leave play on their own.
When a permanent phases out, it leaves play and is set aside, much as if it had been removed from the game. Any enchantments on the permanent phase out along with it. The permanent also keeps any counters it has as well as any permanent changes that have been made to it. Otherwise, all effects that depend on that permanent being in play or that apply to it while it's in play end immediately. All damage on it is removed, and because it's considered out of play, any effects scheduled to affect it at end of turn are ignored.
A permanent that's phased out will phase in (that is, return to play) at the beginning of its controller's next untap phase. Note that if might or might not enter play under the control of that player, as only effects that gave control of it to someone permanently will remain on it when it phases out. When a permanent phases in, it enters play tapped if and only if it was tapped when it phased out. (In other words, it enters play tapped as appropriate instead of entering play untapped and then becoming tapped.) Effects that would normally trigger as the permanent comes into play are ignored. Permanents phase in without summoning sickness.
A permanent with phasing phases out automatically at the beginning of its controller's untap phase, at the same time as other permanents would be phasing in. It doesn't phase out on the turn in which it phased in.
If a token phases out, it's removed from the game entirely, because it has left play.