Phasing is an older keyword that has gone through a few changes over the years in order to keep the ability from being too powerful or just so it would work within the rules. At this point the specifics of how it works is somewhat different from when it was originally introduced, but as a whole it works at intended.
The short version of how phasing works, at least as originally intended, is that permanents with phasing are only in play every other turn. At the beginning of a players untap step, permanents that this player controls in play would ‘phase out’ and those that that previously phased out under this player’s control would phase into play. There were a few abilities and effects that would cause a permanent to phase out, but that only changed how and when a permanent would phase out.
One of the recent and biggest change to Phasing is the elimination of the phased out zone. Permanents no longer leave play and reenter play when they phase, they remain in the battlefield, the game just treats them as if they are not there at all. Unless an effect specifically refers to a phased out permanent, any effect that would normally apply to it will ‘not see it.’
In the past phasing was altered so permanents that phased out didn’t trigger enters the battlefield abilities, but would trigger those on a permanent leaving play. Under the current phasing rules, neither of those two types of triggered abilities will trigger as these permanents do not leave or enter play.
Because phasing doesn’t cause permanents to go to a new zone, tokens that phase cease to exist when they phase out. How this works is not any different from in the past, but the rules that make this happen are a bit different.
For the most part, the rest of phasing works the same as it always has. Auras and equipment attached to a permanent that phases out will phase out with it. When a permanent phases out all counters on it remain and continuous effects with a duration can end when the permanent they effect is phased out.