Gaining Skill PointsEdit
Skill Points are awarded after each successful fight to all party members. Yes, all, even those not yet unlocked or temporarily out of the party. When you get those party members (back), you probably see a significant amount of unspent Skill Points.
Spending Skill PointsEdit
You can only learn the next Stat bonus or Skill on your skill tree, with the eventual choice between two Stats at every grey node (5 times per tree). Once you finish a tree, you can immediately unlock a new one.
Even though the SP costs increase as you progress, it is compensated by the SP rewards for fighting tougher opponents, so all characters can advance after a few battles.