Attributes, Proficiencies and Skills.

Skills:
These are the actions.

Flaming weapon (magical).
The flaming damage makes the mage a formidable combatant if he can only get in the first strike. Having this available, he's suddenly a lot better able to branch into a warrior style. Or maybe a warrior wants to expand his reportoire.
Requirements: Battlemagic 5.

As you can see, somebody with 1 in the related magic stat will not be able to start with this. A fighter would start somewhere else in magic.

Brute power (magical).
The strength of the caster increases by 1 for the duration of the spell.
Requirements: Battlemagic 1. (And no proficiency starts below 1).

Casting this spell gains the character experience in:
Magic (general).
Battlemagic.

Attacking will function as normal (learning not altered by spells).

UNDEFINED SPELL DURATIONS:
Spells might be set to drain X mana / time unit, and be activated/deactivated.
Like "embrace shadows" does to vitaliy.

Attacking is a skill unto itself, but everybody has this very basic capability.
It is therefore disregarded on the skill tree.

Acquiring skills:
A tutor or a book can offer the ability quite fast.
To learn it by book, you must fulfill the requirements.
If you learn it by tutor, you need not fulfill them, but can not use the skill yet unless you do. (Can learn for future needs).

To learn a skill without a tutor, you must forgo all 'attribute training', and practice the skill instead. You must have the required proficiencies, and train for X days straight (X being defined for each skill).