Another way to word it --
Grab the big pipe by the bell at its balance point (as described above) with the bell straight down, and your right palm facing away with the thumb pointed to the ground.
Give it a kick with your left hand, spin it, catch the bottom pipe with your left hand, and put it on your shoulder.
"Helicopter" spin:
Just like above, except start with the horn horizontal. You can be carrying the horn at waist level, or you can pick it up from laying flat on the ground.
VERY IMPORTANT:
Do NOT try to spin by using your right arm's wrist muscles. Imagine that it is a pivot, guiding the horn through the spin, keeping it from hitting you in the face (or, yes, the ####).
ALSO, the horn is only spinning on one hand for about 270 degrees, not all the way up to the shoulder. Look closely at Scott's left hand in his clip -- it grabs the "shoulder pipe" right about when the horn reaches vertical again. Do this, and you will have control of the horn as it comes to your shoulder. Don't do it, and you're more likely to bust your forehead or drop the horn on the ground.
How to spin in unison cleanly as a line:
(This is a lot easier to teach in person, but I'll try to describe it anyway) --
Most contra spins are done in a ripple for two reasons -- to look cool, and to look cleaner than a potentially dirty unison spin. For a unison spin, it's best to have a count structure. There are four moments during the spin where a hand or shoulder makes contact with the horn, so doing them in sequence 1-2-3-4 will yield a repeatable, clean unison spin.
These "moments" are when you kick off the spin with your left hand, then grab it again on the bottom pipe below the valves, then placement on the shoulder, and finally moving the right hand back to the valves. So, think of it like this:
1. Spin
2. Catch
3. Shoulder
4. Valves
If you watch Scott's video clip, you'll see the "1-2-3" pretty easily.
PS -- Hi, Shawn.. lol