I would first say that since it's about going to parallel worlds that are able to access a desired affect and bring it here, the first thing you would teach would be how to get to those worlds and what is different... essentially, think of it as teaching a multi-dimensional map. Perhaps smaller effects are available in closer systems and you have to travel further for more desired effects. It will take more energy to access a realm that is further away from us than one that is closer too us. Perhaps you can short cut through realms. Realm A cannot access Realm Z directly with all the manna available in either one Realm. However, Realm A can accesses Realm B and for a very payable fee, short cuts into Realm Z. More short cuts still require more energy, but not nearly enough as a direct link. This makes the need for a location lesson and a pathing lesson. Think of it as opening a file on your computer for the latter and think of the former as knowing where the file is in relation to another file... assume a very disorganized filer.
Another option that I'm working on is that "magic" is essentially a rule system that doesn't operate on the rules of logic as we know it (actually, the logic as we know it is itself just the most commonly accepted for of magic). Thus, the lesson isn't about the formula but learning the mindset of the logic behind the effect... this allows for creativity as the making it work part is more on the mindset of the spell user than the actual spell and allows for specialization. Magic works because you reject the logic that says it should not work and thus accept that the world will work differently under your new logic. In this system, I use the forllowing example:
Given (i.e. the situation): A door with no windows that that is unattached to any walls standing in the middle of an empty field.
Prove (i.e. Magical outcome): It can open to another location not near the present one.
Proof (i.e. The spell):
- Magic exists.
- All doors facilitate travel through otherwise unpassible barriers.
- A door's function relies on an unpassible barrier.
- All doors must have an unpassible barrier.
- If a barrier exists but I can walk around this door without being stopped, than the barrier must exist in some form that I do not percieve as having height, length, or width.
- If it does not have those things, than the barrier exist in directions I cannot comprehend.
- If it exists in directions I cannot comprehend, than by passing through this door, I must pass through in a direction I cannot comprehend.
- Therefor, if I can comprehend this direction I can get to the room on the otherside, no matter how thick the barrier.
- Since Magic exists, magic will allow me to comprehend this new direction.
- Therefor, there is a room on the otherside.
- Therefor, I shall open this door, enter in the correct manner, and go to the room on the otherside.
- Therefor, there is a room on the other side of this door.
At which point, your wizard/witch can open the door to a wizarding bar. And by knowing this spell, the wizard or witch can thus prove its possible and thus make their own version.
If magic revolves around moving stuff between an infinate number of dimensions, there must exist a dimension where your desired outcome happens. If such a dimension exists, you must be able to reach it. If directly reaching it is impossible given the manna, than I can reach it by way of a path through other dimensions. Therefor, I need to know that the dimension exists (i.e. the result) AND the path (i.e. the spell).
Compared with Harry Potter: Magic there has very little described rules because the purpose of the stories wasn't how magic works, it was that it works and here's all the adventures that happen with that in mind. You want a world that relies on the mechanics of magic to work in a particular way because its essential to see why something that should be impossible is possible. In Harry Potter, the rule was you wave a wand, say a funny word or words, and something happens. Here, it's not so much what you do and say that makes it happen, by why it happens. In Harry Potter, magic is a science. In systems that describe why magic works, it's a rejection of science. There are less rules and more cleverness to get around the few rules that are.