I worked up to doing spins by learning to make very tight 'leaning turns' (as opposed to action/reaction turns). Just start a leaning turn and make a circle, progressively shortening the radius. Don't try spins until you can make a 1 meter circle. As a rule of thumb, the tighter you turn, the more you must lean, and the more your center of gravity must lead the wheel.
You will know when a spin happens.
Suddenly turning will become much easier and you will make at least two circles before you know what's happening. It will feel like you are pedaling twice as fast as you should be. I think the wheel must do a complete revolution for each 360 degrees of spin. You will feel your tire scuffing against the pavement too.
Here's what happens: Imagine riding around in a circle, and a vertical line drawn up through the center of that circle. As you start riding smaller circles, shortening the radius and leaning further into the turn, soon you get a point where that vertical line starts traveling through your torso. At some point that vertical line is going up through your body quite close to your own center of gravity. Then part of your body (your head and at least one of your shoulders) is on one side of the vertical line and starts to balance out the part on the other side. While your wheel is doing a circle on the ground, your head is doing another (smaller) circle in the air, the same direction but 180 degrees out of phase.
Step 1: Do this by tipping your hips inward (to tilt the wheel) and leaning forward slightly to lead the wheel with your center of gravity. Your torso and head lean away from the turn to partially balance the displacement of your hips. Your spine and the unicycle frame should make a < shape pointing to the center of the circle.
Step 2: Basically lean, twist and trust the wheel to follow. Spins to the left work best for me--is this Coriolis force or just personal preference?)
Step 3: Your arms are in line with each other. The inside arm points at a spot on the circumference of the circle made by the wheel, more than 180 degrees from where the wheel makes contact. The < shape of your spine and the unicyle frame will tilt inward until your spine is almost vertical.