Step 1: Boom
A boom is quite necessary for beginners, as trying to learn barefooting on a long line generally results in heavy bruising and very little successful barefooting.
Step 2: Practice on the boat
You'll start planing off on your stomach/hips, holding the boom. First, flip your body around so you're riding on your rear end. Bend your knees and angle the kneecaps towards the back of the boat, such that you're riding on your left hip. Now, use those abs to scoot your body around so that your feet face front. Brace your knees solidly together, and SLOWLY roll forward so that you transfer some weight to your feet; this is the three-point position. Transfer more weight to your feet, and let the force of the water pop you up, and you'll ride like you're sitting in a chair.
Wasn't that easy? Now, hop in the water and let's try it faster and with spray.
Step 3: Plane off and flip onto your back
Remember our dry-land practice? You'll plane off on your stomach/hips while holding onto the bar, then flip your body so that you're dragging along on your backside while maintaining the same grip on the boom. Pretty simple, really.
Just ignore all of that spray and the bouncing; the padding in your wetsuit will prevent any visible damage.
Step 4: Bend your knees, point them back, and spin on your left hip
Scooting around on top of the water is relatively easy; once you get going you can slide like you're on ice. However, if you catch some of that water moving past you at 30mph it will seriously slow you down.
Planing on your left hip raises the front hip, meaning that you can't catch a lapful of water while you spin around. Check out the pictures below to recognize the difference.
So: bend those knees, shift to your left hip, then use those abs to spin your feet around towards the front. Make sure to keep your front hip high all the way through, else you'll catch water and have to work a lot harder. A nice fast spin is cleaner, and produces less spray.
If you do catch water and get your feet tossed behind you just keep hold of the boom, plane off on your stomach again, and repeat the process.
Step 5: Knees together, feet apart, toes up- and SLOWLY into three point
Thankfully, you remember that dry-land stuff again: clamp your knees together and spread your feet, making a rough equilateral triangle. Make sure to pull your toes up so they don't catch and angle your toes in to direct spray out.
Now, maintain this position and VERY SLOWLY roll yourself forward and incrementally transfer weight to your feet to achieve the three point position. Do not try to 1) move quickly, or 2) straighten your legs, or you will catch your feet and land HARD on your face. Your feet are (probably) a much smaller surface area than your butt, so there's a bit of adjustment to be worked through in the process. You can go for a good bit with both your feet and your butt in the water, so don't stress it.
In addition to providing foot stability, keeping your knees together has another benefit: it helps keep spray out of your face. This is key to being able to see ANYTHING at this stage. Also, turn your toes inward and press out a bit with your feet to direct spray away from the face; when you learn to do this properly you can avoid spray even with your knees apart. See pictures below for an example of a knees-apart, flat-footed barefooter eating spray.
Eventually you'll plane off on your feet and it will start to feel comfortable enough that your rear end will naturally come up out of the water as you transfer more weight to your feet. The proper barefooting position on a boom looks an awful lot like sitting in a chair: your thighs are roughly parallel to the surface of the water. You can move from side to side by adjusting the weight you place on each foot; pressing down with your left foot sends you right, and vice versa. It's just like shifting direction on skis.
Again, if your feet get ripped out from under you and you can maintain a grip on the boom, just plane off on your stomach and try again. However, if you botch the feet-in part you will likely be splatted on your face quite efficiently, and will have to wait for the boat to circle for another try. This is why the neck brace can be handy while learning.
Step 6: Add a short rope- tumble turns
First change the angle of the boom: it needs to be higher off the water to accommodate the change in angle from the short rope and give you room to maneuver underneath.
Use the same technique to plane, spin, and stand as when holding onto the boom directly. When spinning, pull the handle in towards your torso to help pull yourself around. Alternatively, get up holding the boom then transfer to the short rope after you've planed off.
With the rope, you can try tumble turns. This is essentially the same motion you used when getting up the first time, except you start and end in an upright position. Drop back into your three-point position, pick up your feet, angle those knees toward the back of the boat, spin 360, and hop back up. Easy, right? Right. Try it until you get the hang of it, and remember exactly how good this is for building those six-pack abs.
Use the rope to your advantage; first, pull the rope in towards your hips as you're facing forward, then pull it towards the side you wish to turn. As you spin, keep the handle right around your belly button; don't let it float too far away from you. As you come around, pull the handle toward the opposite hip, then back to the center as you return to your three-point position.
Remember that you keep your kneese pointed to the back of the boat to keep from catching a lap full of water; this involves swapping directions halfway through the tumble turn. See pictures below.
Step 7: One-footed
Stand up as normal, scoot your feet a bit closer together, shift your wieght onto one foot, then... slowly slide the other foot forward then up and out of the water. The remaining foot will of necessity center itself a bit more to adequately support you. Slide your foot back into place slowly, then redistribute your weight.
If you're doing this on trick on the short rope, turn the handle towards the foot that's going to stay put, then follow the boom instructions above.
Expect to clean out your sinuses thoroughly until you get this (or any) trick down properly.
Step 8: Jumping
First, practice "upweighting": squat and raise yourself back to the standard barefooting position. This gets you used to weight shifts on your feet. Work up to deeper squats and more propulsive upweights, then you'll be able to naturally progress to small hops.
Once you're properly up and going, ask the driver for a bit more gas then... jump. It's just a more dramatic form of the upweighting you've been practicing. Push down on the boom to get some properly impressive air. Now comes the hard part- landing! You've put your feet in before; this is the same, just faster, so be sure to do it right. Wasn't that helpful? Now, try it again. No, again. Er... maybe it's time to try more upweighting.
Step 9: Advanced technique: direct to kneeling position
Once you've got those abs properly developed, it's possible to pop up directly from your stomach to skiing in a sitting position with your legs tucked under you. If you've practiced jumping, this is a similar technique: push down against the water and raise your torso, then use this additional space to QUICKLY pull your knees toward your chest. If you manage not to catch your knees in the oncoming water, you should find yourself essentially sitting on your feet, planed off on the top of your feet and ankles.
From this position you can roll onto your rear end and get up via a three-point position, or for bonus points you can execute a truly impressive jump and land on your feet. If you're going for the latter, definitely work on the upweighting first and try not to catch your toes on the way up.
Step 10: Hand skiing
First, up you go on the boom, then transfer to the short rope. Sit down comfortably on your rear end, stick one of your feet in the foothold on the handle, adjust as necessary, then tense up your abdominal muscles and let go with your hands. Lean back; it's all on your foot. Curl your toes up a bit to keep from sliding out of the foothold.
Now, take a deep breath and flip onto your stomach, facing the back of the boat; the handle will spin with you. You're going to get a lot of spray in your face, so arch your back, pressing your chest into the water, and pick your head up to breathe in the spray-free air pocket you've created. Put your hands under your nipples, and... do a pushup. The water will be trying to push your hands out from under you towards your sides and the back of the boat, so maintaining this position will require some serious effort from the triceps, lats and pecs. Work hard to keep your hands from drifting outside your torso. Keep your head up and out of the spray.
To return, reverse your pushup, spin onto your backside, sit up, and grab the handle again. Wasn't that fun?
Step 11: Move on to the long line
In the meantime, Ben suggests that you check out http://www.barefootcentral.com/cool.htm for inspiration, particularly Andre De Villiers "Goin Too Fast".