Most of my out-of-the-saddle time is spent climbing: either to take a break from pedaling in the saddle, or to get through a steep section. I've been doing it so long that I've had to think about what I do to put it into words, but here goes:

1. Straighten out the lower back, and lengthen the torso. That's number one, because the back needs a break. I can feel the tension release within a few pedal strokes.
2. Keep a light amount of weight on your hands by maintaining your hips close to the saddle nose.
3. Gently rock the bike from side to side. Don't rock your shoulders.
4. Pedal a low cadence by shifting up a gear or two. This will keep the aerobic effort roughly the same.
5. Don't bounce your hips up and down.