I've taught ice-axe skills several times both professionally and casually. I would advise to be sure and learn all of the aspects of snow climbing in order of importance, not just practice self-arrest alone. I generally find a slope with a safe run-out and have people do the following. The initial lessons should all be done without crampons so that people don't stab themselves with the points and rip up there clothes.
Leave the axes at the bottom of the slope and practice kicking steps with your balance point over your feet. Practice all of the steps, strait-in, side-stepping, duck-walking, traversing, changing from one direction to the other on traverse, and plunge stepping. Do this a lot, climbing in balance with good footwork is the key to avoiding falls in the first place, and it is always better to not fall. Climbing without falling is plan A, try to make get good enough with your feet that it's what happens.
Have people pick up there axes and hold them at there sides in the self-arrest grip. Have them walk on level ground, moving the axe so as to stay in balance. It is the opposite motion to how you use a trekking pole.
Have them practice all of the footwork again plunging the axe so as to stay in balance. Practice switching hands and changing directions on traverse. The point is to develop movement patterns such that people can climb without falling.
Demonstrate self-belay, holding a fall with the shaft of the axe plunged into the snow. Have everyone practice this, usually first while traversing and than with the other footwork. The ideal technique is where as your feet start to slide you turn and deliberately fall onto the head of your axe, driving it into the snow. Practice it until everyone is comfortable and confident. This technique is safer than self-arrest because you don't build up as much momentum, and also because your plunged axe-shaft is typically a better anchor than the pick.
Than move on to true self-arrest. First practice rolling toward the head of the axe on level ground with the axe on each side. Than go strait up the hill, turn around, sit down and start sliding. Roll over and arrest. Repeat, repeat, repeat, until it is easy.
I teach a technique that works with or without crampons. You roll onto the axe with your knees bent and feet in the air, than actively pull-up on the axe shaft while leaning hard on the head. You stay in that position until you slow down to a very slow speed, than you forcefully kick your feet in for your final stop. The key is that you slow enough with your feet in the air that by the time you kick you don't have enough energy to hurt your ankle. It is also important to practice getting up from the self-arrest position without falling again and getting back in balance.
Move on to the other positions. The head-down on your back sometimes requires that one person holds another's feet.
I find it's often helpful to put in a "sled track" that no one kick's steps in and have people take turns in it because than it's easy to get up some speed.
After everyone is comfortable with all four positions in the sled track, everyone than tries it with a pack on. Often times it seems easier because the pack provides extra drag.
Everyone should practice self-arrest without an axe. In softer snow it often works better. I usually just to it from one position though.
Than I usually have people practice all of the climbing foot-work again except with a hiking pole in the hand opposite the axe. Practice switching both to keep the axe up-hill.
At some point near the end of the process there will usually be a moment, preferably surprising, where I grab the students and push/throw them down the hill. Being caught by surprise and possibly having the wind knocked out of you is very realistic and I think important.
The above activities usually take all day.
If glacier travel is in the cards, rope-team practice is a whole other lesson. Keeping the rope tight through various manoeuvres is important, and I do like to practice team arrest. If you can find a good slope you can get one person on the rope sliding quite fast.
I am inclined to do all of the above without crampons on, because I don't think you do much of any of it differently with crampons on. Crampons often make it harder to fall and easier to be secure in your steps, so people don't develop good balance, footwork, and ice-axe skills as quickly. When people are learning to walk and climb in crampons there is generally a lot of shredded gaiters and pants, as well as the falls that go with that, so think it's better if they already know the other stuff. It is certainly easier to hurt yourself falling with crampons than without, although honestly in the conditions you practice in it's not so much a worry about a broken ankle as about cuts and stabs from the points.
Note that the above describes basic technique. There are a myriad of other techniques I use for getting up and down snow and ice slopes in the mountains and stopping falls using axes and crampons that vary from the above in significant ways, but this is the foundation of skills that will allow one to learn all of the other techniques.