The what/how thing is pretty spot on. Magic abilities will focus on how's, with specific what's being improvable as specialties (e.g., Harry knows the 'how' of Evocation, and has some tools and skills improving his ability with the 'what' of throwing fire around).
Magic largely breaks down into:
Common ritual - The magic that everyone can do, so long as they get their hands on the right (usually rare, protected) tome containing rituals that haven't been ground down to uselessness by overuse.
Evocation - Grossly simplified, this is the ability to summon up a bunch of energy of type A, and push it somewhere. It's very fast, and it resembles magic that's been done all over for thousands of years. Big supernatural creatures have had evocation and evocation-like things for a long damn time, and by and large it's the main way they get things done, magically (beyond the abilities simply contained within their bodies, like supernatural strength, yadda yadda). Wizards tend to know a wide variety of techniques within Evocation, while others may be limitd to a specific technique or two (such as the "telekinetic" kid, who's actually a budding kinetomancer).
Thaumaturgy - This is the ability to construct very potent ritual results, and is one of the few big edges that mankind has when it comes to spellcraft. This is the ability to do things that are vastly more subtle than human Evocation tends to allow, as well as things that are vastly more potent, thanks to the elements of structure and control that it can bring to a party. This has also given rise to the creation of objects that resonate with or store particular kinds of magics, so it's where you'll find your blasting rods and potions getting created ("Alchemy"). In general, Thaumaturgy lets magic do things that aren't dependent on pushing energy in a straight line from point A to point B, and it lets you combine several kinds of energy into the same thing. It is, in short, everything that Evocation isn't.
