Left/Right moves left right.
Fire/Action Button Jumps.
Down and Action button when standing still spins you up. Let go of the action button to let Zippy go!
I was originally going to have rings explode from Zippy when he got hit by an enemy but with the enemy still on screen I found it rather impossible to do, so here's my work-around. When you get hit by an enemy, the enemy "steals" your rings. To get some of them back you have to "pop" the enemy. Once the enemy goes off screen, so does the possibility to get your rings back.
Getting to the mid-point of the level will automatically set your checkpoint.
Use the springboards to get to the upper half of the level.
Everything else you'll need to find out on your own.