You will receive one training point every 4 levels till 20. This means you will receive them at level 4, 8, 12, 16 and 20. After level 20, you will receive one training point every 5 levels. You can also receive training points through certain quests. In order to learn higher level spells of a school, you have to first learn the lower level spells.
If you make a mistake, visit Mr Lincoln in Golem Court. He will let you buy your Training Points back with Crowns, and you will lose those spells. You must be at least level 12 to buy back your Training Points. This transaction costs Crowns.
If you want the prize, you have to build the ladder rung by rung. There are no shortcuts.