The one thing I see most neglected in teaching a roundoff is the entry -- that is, the hurdle and lunge.
Different coaches have different preferences regarding how high or long a hurdle should go, but there are two key things that I think most coaches will agree on:
1. The hurdle should push forward; it should not go for height at the expense of forward momentum
2. It should land in a long, low, deep lunge. The lunge is almost always overlooked, but that is the primary source of a tumbler's power. The front knee should bend deeply, so that the gymnast can start lower and get her hands to the floor quicker. This also allows the gymnast to get a better push off the front leg, and a better drive with the back leg.
For younger kids I like to teach a roundoff going off a pannel mat to help them come off hollow/straight instead of piked. Great points GT about the hurdle and lunge---a lot of people don't focus on those enough. I also like to concentrate on the first foot and reaching to put the hands down--a lot of kids like to put their hands right next to their foot.
Good Handstand. Great HS. Good shoulder flexibility. This will take a long time. I remember a neat drill is to get into handstand and straddle the legs. Spot them rocking from one hand to the other. This is a real pain to spot at lower levels.
Awesome cartwheel. Master a side cartwheel. Master a lunge to lunge cartwheel. Master a cartwheel step in from a side cartwheel and a lunge.
Directly vertical, no arch, body in a straight line from ankle to wrist. Push through the shoulders. Lunge deeply.
One of my pet peeves. Learn how to lunge through it. Always start in an appropriate distance lunge.
Do all basic tumbling like this on a line. I use the carpet seams. Right foot stays on the right side of the line, as does the left. Hands stay on the line. They should fix that sometime after compulsory...ha-hah. Seriously, you'll be watching them cross one leg over the midline and contributes to funky tumbling. That and head out.
Late snap of legs together in the cartwheel step in is basically the round off.
Block off the hands. Snap down/through hard.
I teach the floor RO as the far hand would be outside of the line instead of on the line. T-hand. I teach the T-hand once the lunge to lunge cartwheel is decent enough they can focus on it.
If they can't handstand snap-down/through...that phase of the RO will be weak.
I've heard about arching into the RO to create more snap and actually aligning the hands a bit differently through the midline. However, I rarely teach it with most kids I have till everything is super.