#New skills, Innate Magic for SLAs, Ki Magic for monk abilities, and a skill for each school of magic according to each tradition (spell list). So a wizard might have Magic (Conjuration [Arcana]), but if that wizard also knew bardic magic (either from multiclassing or study for casting from a book, explained later) then that would be Magic (Conjuration [Spellsong]).
No need to notate the default tradition of your caster, unless multiclassing. Really noting the tradition difference is only important if trying to multiclass multiple casting classes or learning to cast by the book for spells outside your normal list.
#Characters gain a Magic Bonus stat that progresses like BAB, save according to their magic. Full casters get +1 per lvl, medium casters (up to sl 6) get 3/4, low casters (sl 4) and characters with racial SLAs and monks get 1/2, while noncasters get 1/4.
#A caster, upon taking their first casting class, chooses to either be a spontaneous caster, or a prepared caster. A spontaneous caster has a spells known list, each slot on the list takes a number of days of study to swap a new spell into, during which time that slot is unusable. Spontaneous casters also get a +2 to their MB.
Prepared casters need to prepare spells each day. If a spell stays the same they still need to reinforce it in their mind by preparing it again. If they do not, then 24 hours after it was prepped, the spell becomes unstable, and when cast there is a 50% chance it fizzles and that spell is forgotten from memory. Prepared casters get a +2 on skill checks to cast spells from memory.
Classes that are normally prepared but have chosen to be spontaneos casters, get a number of spells known according to the sorcerer's spells known table.
Even if you multiclass, you can only be either a spontaneous or a prepared caster. Prepared casters basically work like the arcanist, save their number of spells prepared is like normal for their class. This means that a prepared caster prepares a list of memorized spells for the day, but can cast them in any order and as many times as they may choose. However, the spells must be prepared each day. If a caster does not prepare spells for a day.(or gets interrupted), they keep their previous list of spells but each time they cast them there is a 50% chance the spell fizzles and is forgotten.
Classes that have spontaneous options, such as cure spells for clerics, always have those spells known or prepared without consuming spell known/prepared slots. Prepared casters do not need to worry about these spells becoming unstable either.
# There are two ways of casting, from memory (the normal way of casting), and from a spellbook. A spellbook can take many forms, from a fat tome of arcana, to scrolls of spellsong, to prayer knots, etc. A spell must be memorized to be cast from memory, and normally only casting classes can memorize spells.
Anybody can cast from a spellbook if they have the appropriate trained skill, even non-casters. Casters can use this option to cast spells from outside their spell list, but a caster still cannot memorize spells from outside their spell list.
Casting from a book takes ten times the normal casting time, and anyone failing the strain check takes triple the strain of the spell lvl, and on a success a noncaster takes twice the strain of the spell lvl. (yes failing is the same for everybody, but only noncasters lose twice the strain on a success.)
Spells have two new values, complexity and drain. These are based mostly on the spell's level after modification by metamagic or similar. Complexity is equal to 4*SL plus 15. Drain is 5*SL plus 5.
To cast a spell, you must roll two things, unless certain conditions are met.
First, you must succeed on a Casting check or the spell fails in some way, whether fizzle or unexpected effect or something strange. A casting check is a skill check of the appropriate Magic (school [tradition]) skill against the spell's complexity. If the skill bonus plus 5 meets or exceeds the Complexity, then this roll can be assumed to be successful. Of course, no critical success without the roll. If the roll is made, then there is potential for a critical success, which improves the DC of the spell by 2 and the CL by 2 (for free). A critical failure however, gets an unpleasant surprise.
The second check is a strain resilience check. The strain check is the core roll plus your MB and your con modifier. Additionally, any strain points earned, normally reduce this result. Occasionally, bonus mana power can reduce strain below zero. Negative strain can indeed provide a bonus to this check. If this check succeeds, the spell goes off, if it fails the spell fizzles, or peters out without significant effect. A critical success grants a +2 to DC and CL (and yes, critical success on both complexity and strain stack.). The base DC for this check assumes a CL of 1. The CL can be increased by either critical successes or by putting more power into the spell increasing the drain of the spell, for each +1 added to the DC for this purpose, the CL increases by one. When the strain check succeeds, a number of strain are gained equal to the SL. If the check succeeds by 10 then the no strain is gained. If the check fails, double the SL in strain is gained. Cantrips still cost a minimum of one strain. If the check fails by an amount equal to your constitution score, you fall unconscious. If this happens, roll a will save DC 10+ 2*SL, fail and the spell fizzles, else the spell goes off as desired unless it has a duration of concentration.
Note, metamagic and other effects that raise the spell slot used, uses that higher slot for the complexity check, but not for the strain check unless the effects of the spell are raised (such as heighten spell if I recall correctly).