A very common problem people have when first learning to spin is that they come up from the entrance edge to try to start the spin too soon.
Start on a line, in a T position (i.e., your spinning foot in front, with your other foot behind it, turned out so that the instep is behind the heel of front foot). Bend your knees, then push off very gently with the back foot and draw a very small, round circle with the spinning foot, keeping the other leg extended behind you, and looking in the direction you're going. Lead yourself around with a very gentle sweep of the left arm (assuming you are spinning CCW to the left). Keep your skating knee deeply bent until you have completed a half circle and come back to the line. To see if you *really* came all the way back to the line, check your tracings on the ice. You'll probably find that you didn't really come back to the line, even if it felt like you did.
Once your entrance edge has completed a half circle and you are back at the line, straighten your knee just a little and lift up onto the bottom pick (the very first pick, just in front of the ball of your foot, so that you feel it scrape just a tiny bit), and pass your free leg through to the front, lifting the thigh once it's in front. Hold your arms at chest level, rounded like you're holding a beach ball. You should be spinning on the round part of the blade just behind the bottom toepick. It's OK if your bottom toepick actually scrapes the ice a little during the spin.
You also might want to check your blades to see if the shape has been altered from bad sharpenings. The part of the blade right behind the toepick should be round, not flattened. Compare your blades to a pair of brand new blades of the same type and see if there's a difference in shape there.