Each Aura and Equipment attached to a permanent that's phasing out also phases out. They will phase in with that permanent and still be attached to it. Similarly, permanents that phase out with counters phase in with those counters.

In a multiplayer game, if you leave the game after Teferi's last ability resolves but before your next turn ends, its effect lasts until your next turn would have begun. It neither expires immediately nor lasts indefinitely.

Phasing out doesn't cause any “leaves the battlefield” abilities to trigger. Similarly, phasing in won't cause any “enters the battlefield” abilities to trigger.

Any continuous effects with a “for as long as” duration such as that of Awakener Druid ignore phased-out objects. Any such effects will expire if their conditions are no longer met after ignoring the phased-out objects.

Any one-shot effects that are waiting “until [this] leaves the battlefield,” such as that of Kitesail Freebooter, won't happen when a permanent phases out.

While a permanent is phased out, it's treated as though it doesn't exist. It can't be the target of spells or abilities, its static abilities have no effect on the game, its triggered abilities can't trigger, it can't attack or block, and so on.

Normally, phased-out permanents phase in during their controller's untap step. Teferi's last ability causes the phased-out permanents to not phase in until the duration has expired; they'll phase in during their controller's next untap step after your next turn.

Choices made for permanents as they entered the battlefield are remembered when they phase in.

An attacking creature that phases out is removed from combat.

Any creatures that phase in during their controller's untap step will be able to attack and pay a cost of during that turn.

If an opponent gains control of your creature and it phases out and the duration of the control-change effect expires before it phases in, that permanent phases in under your control as that opponent's appropriate untap step begins. If they leave the game before that untap step, it phases in as the next untap step begins after that turn would have begun.