Kayato: So I'm trying to understand how skill points work.
I understand that they determine how much mana I can use in a fight and how many turns I use to cast a spell, but keeping the red staff at zero I have no problem casting spells.
Now I have 25 SP with the red staff at zero, why?
If I want more SP I should move the staff more than 25?
Each turn you get a number of power points, and those power points are distributed to the three wands each turn. Power comes from things like nodes, citizens of certain races, and religious buildings (ex. shrine).
The first wand is Mana. Any spell maintenance you need to pay is deducted from your mana income first, then any remainder after that calculation is applied to your mana stockpile (if you have more mana income than maintenance costs, the extra is added to your mana stockpile).
The second wand is Research. This is the number of research points that is being applied toward your current research target. Libraries and similar buildings will add to this total as well. Any overflow beyond what is needed to finish the current spell is lost, so you can see some savings by monitoring your progress and not overspending on that last turn.
The third wand is Skill. Power spent on this wand affects how fast your spell skill grows. You need to spend a number of points on this wand equal to 2x your current casting skill in order to gain a new point of casting skill. Any power spent on this wand is not lost; if it takes you several turns to spend the necessary power, that's fine. If you need to reduce expenditures on Skill for awhile, then do so, but it is useful to keep this as high as you can afford to keep it. Sadly, there is no way to see how much power you've spent on this wand. The +10 spell skill from Archmage is NOT included when calculating how much power you need to spend to raise your spell skill.
Your spell skill is listed below the three wands. Any heroes that are staying in the city with your wizard's tower will add their spell skill to yours for casting spells (with some limits; they don't make spells Instant). This is the value that increases as you spend power points on the Skill wand.