How they work is you select some ships in one gravwell with a phase stabilizer, and you right-click a second, different gravwell with a phase stabilizer in it. Your ships will then proceed to the edge of the first gravwell that is closest to the second phase stabilizer and fly to it, even though there is no visible "phase lane" between the start and finish. You don't have to select the phase stabilizer or move closer to it or anything - that's all handled automagically.

Some notes:
- Phase stabilizers must be 100% completely constructed before you can fly between them.
- No antimatter is consumed.
- Various upgrades can really speed up your passage while in phase space.

-- Retro

Sorry, to clarify, I meant no antimatter is consumed IN THE PHASE STABILIZER. The ships still lose their standard antimatter penalty from phase jumping.

-- Retro

they all aren't in the same grav-well....anyway i was also wondering about playing online...do you need just this login and stuff or do you sign up again? and you need the Disk in for that the first time or every time you play online?

Keep in mind they also only work in the same solar system, you can't phase from one star to another with phase stabilizers which is quite unfortunate but I suppose would make the vasari just a little too mobile.