Disengagement is an art, not a science. But, if you insist on treating it as a science, here's a primer.
Technique One: The Art of the Nonchalant Exit - The classic "I'm just going out for a walk" disengagement.
Technique Two: The Sudden, Unannounced Departure - The "I'm outta here" disengagement.
Technique Three: The Fake Phone Call Disengagement - A timeless classic.