I am currently working on a skibike instructors' teaching manual, but if you want a flavour of what you would learn during skibike lessons, read on...
1. Induction - Becoming comfortable with a skibike
You should get the opportunity to familiarise yourself with the construction, balance and weight of the skibike. It is a useful experience to try lifting, pushing and carrying it around. You should be asked to try it whilst stationary on a level surface both sitting and standing on the pegs.
You will be surprised to find that unlike a wheeled bike you can sit on the saddle perfectly balanced with your feet on the pegs. Your instructor may ask about your prior snow experiences and abilities, don't be shy, they just want to make sure you get the right level of instruction at the right time.
2. First Run - Learning how to brake
As with all other snow sports learning how to stop is your first lesson. You should be taken to a safe easy slope and will walk up the slope either pushing or possibly carrying the skibike.
Your instructor will show you the skibike equivalent of the ice hockey stop. You will need to practice this a few times until you feel confident with the movement, both your safety and those of others depend on it.
3. Getting Up The Hill - Walking is too much effort
Next you will need to get up the hill, this could be by; cable car, chairlift or even drag type lift. Youshould be shown how to do this safely without causing other snow users inconvenience.
4. Linked "Hockey Stops" - Thrills start here
You have already discovered the basics, now let's see you put them into practice. You should be able to get down an easy slope by just using a sequence of linked hockey stops. Don't be surprised if turning one way is easier than the other, almost everyone is built that way. Your confidence on the skibike should already be growing and preparing you for more advanced techniques.
5. Side slipping - Moving onto intermediate level skibiking
Your instructor should take you through some exercises to learn how to get the bike skidding sideways down the slope. This is a unique skibike sensation which can be great fun and prepares you for the next stage.
6. Linked drifted turns - time to be a hooligan
Now it's time to combine both of the previous lessons and have a lot of fun too. Your instructor should take you on a relatively easy and long run. Here he should demonstrate how you can drift a skibike by combining elements of both the hockey stop and side slipping techniques.
Get this right and riding a bike on wheels will never feel the same again.
7. Carving - Moving up to expert level
As your speed increases you may find that drifting becomes more difficult, if this is the case you are ready to carve. You should be showed how to tilt the skibike whilst keeping your upper body upright. The instructor is likely to take you to a steeper groomed slope and get you to try carving, don't be surprised if the acceleration surprises you. Remember that you can still hockey stop or drift back to a dead halt if you need to.
8. Off Piste - Heading into the unknown
Skiing on prepared snow is fun, but for many once they have gone into the rough stuff there is no looking back. Best of all, off-piste skibiking is much easier to learn than skiing. Your instructor should take you to an area of unprepared snow and show you how to adjust your stance and riding style. In the right conditions the sensation will be like low altitude flying, some have compared it to jet skiing. Try to keep going at all costs, falling off is not usually a problem but getting back on again can be.
9. Jumps - Time for some big air
As your confidence and speed climbs you will find yourself becoming airborne. You instructor should take you to a suitable section of terrain to becoming familiar with leaving the snow and most importantly landing safely. Whether you want to take these skills into the snow park is your choice.
Here's an excellent video from BullSkate that shows the basic moves, yes it's in Swiss German but I'm sure you'll get the gist of it.