Basic Arcane casting Rules V1

What to Roll

Each arcane spell is associated with one of the nine basic attributes:  Dexterity, Strength, Stamina, Appearance, Charisma, Manipulation, Intelligence, Perception, or Wits.  To cast a spell add the spell's associated attribute to the relevant casting attribute.  The difficulty is 6 unless specified otherwise or special modifiers are in play.
For instance Alarm uses Perception + Abjuration and Shield uses Dexterity + Abjuration.

Quintessence and how it sets a limit on what you can cast

If your character is an arcane caster, your maximum Quintessence pool is pool is your (Willpower + the sum of all your casting attributes) x 4.
First Circle spells normally cost one quintessence point. Second Circle spells cost two quintessence points, and so on and so forth. Invocation spells are different. For every two successes you roll (round up), the spell costs one Quintessence point.
Some magical items and familiars can act as Quintessence batteries called periapts. Some familiars can store Quintessence for their mage. Periapts can generally be used by any arcane casters. Familiars usually can only provide energy to mages they are bonded with.
If you have at least one quintessence point but not enough to cast the spell you want, you can still cast the spell at the cost of all your remaining quintessence with a +1 difficulty modifier. A mage with zero quintessence cannot cast any magic at all.
Invocation spells are different. For every two successes you roll (round up), the spell costs one Quintessence point.
Mage can regain quintessence by mediating (Wits + Enigmas), studying a spell book or something similar (Intelligence + Spellcraft) normally at difficulty 6. The caster gets 5 quintessence points per success rolled. This takes about an hour and requires the caster to be relatively well rested and be in a place with few outside distractions. This can only be done once per day.

Some magical items and familiars can act as Quintessence batteries, these are called periapts. Some familiars can store Quintessence for their mage. Periapts can generally be used by any arcane casters. Familiars usually can only provide energy to mages they are bonded with.
Casters can regain quintessence by mediating (Wits + Enigmas), studying a spell book or something similar (Intelligence + Spellcraft) normally at difficulty 6. The caster gets 5 quintessence points per success rolled. This takes about an hour and requires the caster to be relatively well rested and at peace.
This can only be done once per day. A failure lets you try again (taking another hour) A botch gets the caster nothing, and may or may not stop the mage from gaining quintessence over the next few days. but at least nothing explodes.
Casters who sleep near a Node of magical power regain quintessence automatically. Usually 10 or 20 points, but a stronger or weaker source could modify this. If too many arcane casters try this on one source, the effect is diluted and the spell casters gain less quintessence at the storyteller’s discretion.
An arcane caster can push himself to cast a spell without spending Quintessence but risks magical feedback. Magical Feedback checks require the caster has to roll Willpower difficulty 4+ the circle of the spell, plus one for every spell cast without mana in the last 24 hours. Failures inflict a level of lethal damage on the caster. Botches inflict three levels of aggravated damage. This damage cannot be healed by magic, only rest and medical care. A botch gets the caster nothing, but at least nothing explodes.

Learning New Magic

Learning a new first circle spell costs 2 experience points and requires you have at least one dot of of the casting attribute in question.
Learning a new second circle spell costs 4 experience points and requires you have at least two dots of of the casting attribute in question.
Learning a new third circle spell costs 6 experience points and requires you have at least three dots of of the casting attribute in question.
And so on and so forth. You can reduce experience costs per new spells with optional prequisates (see side bar for details)
Learning a first dot of new school costs 4 experience points. Raising dots after the first costs the current rating x3. Casting attribute dots and buying spells is separately though it is common for players to buy these things together.

A character with the Eureka Moments Merit may gain a new spell or a new dot of a magic school at any time as long as they have the experience to pay for it.
(Note the methods below can be dispensed with at the game master's discretion any time a mage takes down time, you can just hand wave that they got the new magic they wanted).

Practice Makes Perfect

Any mage that extensively uses any of their magic, either by rolling it in-game or intense training and practice during downtime can raise their rating of a casting attribute that they already have.
Gaining a first dot of a new school of magic requires research or training.

book Learning and teachers

A character with Spellcraft may research a spell that is known with an extended Intelligence + Spellcraft roll. Difficulty 6 if the spell is on the list, or difficulty 8 if they are researching a new spell altogether. Each roll takes a five or seven days and about 25 gold worth reagents. If the wizard is willing to go through 100 gold worth of reagents per weak, they get -1 difficulty on the roll.
If the researcher has access to an extensive library, they get a -1 difficulty on the roll.
If the researcher has the Book Savant Merit, they get a -1 difficulty modifier.
Humans and other races with relative short life spans can make one roll every five days while elves and gnomes and similar long lived beings take seven days.
First Circle spells take three successes
Second Circle spells take five successes
Third Circle spells take ten successes
Fourth circle spells take fifteen successes
Fifth circles spell take twenty successes
A new dot of a previously unknown school is five successes

If the researcher is not researching a spell from scratch and is researching a spell from another wizard's spell book, the rolls are the same but humans need one day per roll and longer lived species need two days per roll. Difficulty 6 for a spell book from the same magical tradition. Difficulty 7 for a spell book from a similar magical tradition, and difficulty 8 for a spell book from a very different tradition.
If the owner of the spell book is taking the time to instruct the researcher in the spell, reduce the difficulty by -2. If the teacher is a long-term mentor of the researcher, another -1 difficulty.
If the research is done near a magical font, another -1 difficulty.
All difficulty modifiers are cumulative, minimum difficulty 3.
If a mage does not have Spellcraft, he or she may roll just his intelligence to learn a new spell but only if using a spell book or teacher from his/her same magical tradition.
The same rules apply for primitives magical traditions whose spell "books" are not literal books. If the mage does not have a spell-book equivalent they can still learn new magic from a mortal teacher or mentor who knows the spell.
If they don't have a mortal teacher or a spell book, then they have to learn new magic by meditation or otherworldly teachers.

Meditation

Effectively this uses the same system as researching a spell with Spellcraft, but it uses Intelligence + Enigmas instead of Intelligence + Spellcraft and is +1 difficulty higher.
If the area of meditation has an ideal spiritual resonance for the mage and/or the new magic being learned, -1 difficulty.
If a mage is researching a spell via Spellcraft and they get half the successes they need, they can walk away from their studies, do a bunch of studies, and go back to their studies where they left off with no negative issues.
If someone is meditating for new spells and is interrupted, they lose a banked success for every major interruption.

Otherworldly Teachers

Some spirits and Fair Folk can teach mortal mages new spells. This usually takes about a day. Maybe a couple days for a high circle spell.
Learning the new spell is automatic but the mage has to perform a boon for the Fair Folk or spirit in question.

Optional Prerequisites

If you'll look at any of the spell lists, you'll notice a lot of the spells have other spells listed by them in parentheses. These are optional prequisates. For every optional prerequisate a mage has, he can deduct the cost of learning that spell by 1, to a minimum of 1 experience point.
For instances, here is the description of "Fly".
Fly (Feather Fall, Jump): Target flies for 10 minutes per success. Dexterity
Fly is a second circle spell so the base cost for learning is 4 experience points. If a mage wants to learn Fly and already has Feather Fall or Jump, he can purchase Fly for a mere 3 experience points. If a mage has Feather Fall AND Jump, he can buy Fly for a mere 2 experience points.
Prequisate experience point discounts only work one way. If a mage learns Fly and then picks up Jump or Feather Fall, it doesn't matter.
It is also possible to have prequisates that are not spells per se. For instance some spells that influence animals have optional prequisates for having a high Animal Ken rating.
Many Abjuration spells have an optional prerequisate for having magical ability in the thing being defended against. For instance, the spell True Form defends against hostile Transmutation. An Abjurer does not need to have learned any Transmutation spells in order to learn True Form, but an Abjurer that is also a Transmuter can learn True Form at a discounted rate.