I think it is the hardest skill to master in skating. Harder than jumping, at least single jumps. A bad jump is still a jump - a bad spin doesn't really spin.
You have to find the feel of where your spin rocker is under your foot. That's time and patience, trial and error.
Don't look down - head up, and don't be floppy with other bits of your body as they will pull you off balance. Don't be rigid either, but your arms and free leg should be controlled and under some tension while still out then pulled in.
Imagine a pole going down through the top of your head and your middle, into the ice through the part of the foot pressing into the ice on the spin rocker.
Keep your core strong, don't collapse in the middle.
I find warming up with 2-footed spins helps a lot. I like 2-footed spins anyway, for themselves.
If it's a normal spin (i.e. not a backspin) then make sure you push onto a decent FO edge to go into it, and don't rush it - wait for the edge to come round, wait what seems like forever. The making of what would be a 3-turn into a spin is timing that you have to learn by trial and error, to know when to whip your free side round so the BI edge goes back onto itself.
As with every element, try to enjoy the learning of it, relax, and approach it as a sensory experience, which it is.
One afterthought - people who can skate and spin properly usually bring their free leg/foot across the spinning foot and push the free foot down. It's neater and makes the spin go way faster (answering one of your questions about how top skaters spin so fast/so many revs), is ultimately more stable and keeps you more centred, and is essential if you want to move on to a sit spin. Beginner spins are usually taught with the free foot moving in and attaching itself to the side in parallel rather than crossed. My personal view is that while it feels uncomfortable it is better to learn how to do it properly from the start as it is so hard to unlearn the "easier" way later.
