When does the ship leave the table and when does it have to declare that is is disengaging?

Is it the first thing that you do and if you pass the test you're off, or do you move first so that you can try and get close to something that adds to your roll or more often to get away from enemy ships to improve your chances of getting away.  The latter makes it like a special order the prior works well if a ship is then to be punished for failing to disengage it then just drifts forward and can't shoot.  (I can't imagine shutting down systems and trying to hide allows for easily turning them back on and shooting)

What do you guys play, my Blue book is a little unclear.

Should be in the BBB somewhere under Disengaging. You attempt the roll before you do anything else at the start of your turn, IIRC. On a successful check, your ship is removed from play immediately.

Hi,

We play it immediately after the ship has moved.
The idea being that you turn away from any enemy ships and dive towards hopefully some conveniently close cover such as celestial phenomena or a cluster of blast markers.
If you fail the leadership roll to disengage then in fluff terms for the ships crew the first they will know about it is that despite their efforts to on silent running they are still being targeted.
As such if you fail then the ship remains on the board but can take no further action (no shooting. launching ordance)that turn except for Brace for Impact.

Ok. Page 33 middle to last paragraph under Disengaging, sequence is:

1. Ship decides to Disengage.
2. Shipe rolls for Ld at end of Movement phase, using the modifiers on page 33.
3. If pass, disengage and remove ship from the tabletop.
4. If failed, ship remains in play and it "may not fire, launch ordnance or attempt to use Special Orders during the turn." This means includng BFI.