The entire concept of sch, much like the system of merits and tiers, is kind of confusing and hard to explain but massively easy to get once you actually see it, but I'll see if I can't clear some things up.
Lets start with white magic. You naturally have white magic such as cures, protects, shells, raises, reraises, paralyna, poisona, stona, so on and so forth. A white mage can go to their magic list and cast them directly. For a scholar to cast some of these spells however, you need to use a job ability called "addendum: white". It's basically you unlocking the ability to cast paralyna, or raise II.
The same goes for black magic spells. While a black mage can cast all their spells without any prior preparation, scholar gets access to tier IV nukes but can only cast them once they've been unlocked through the usage of "addendum: black".
As far as arts. Light/Dark arts are JA's with a 1 minute recast and a 2 hour duration. They're stances of sorts. Are you gonna be a healer? Light arts is the healer stance. Are you going to nuke? Dark arts is the nuking stance. Casting appropriate spells with the right arts up (cure with light cures, thunder III with dark arts) reduces mp cost by 10%, reduces casting time by 10%, and boosts all your magic skills to a B+ skill level. IE; use the correct arts.
One of the appeals of sch is not only are we more than capable healers and support, if the situation calls for it we're only two job abilities away from being able to drop tier IV nukes.
Hope that helped clear some things up. Ended up being much longer than I intended.