You earn Training Points as you level. You earn one every four levels until 20. Then you earn one every five levels. (See Experience Chart) You can also earn additional Training Points by completing quests.
Training Points can be used to learn spells outside of your school that are not designated as FREE. (See example in image below)
At first, it is generally best to focus all of your Training Points in one school. Later, you will get enough Training Points to start exploring a second or third school.
By Level 50, doing quests that give you additional training points, the total of points should be 17
Training Points Example
In the image to the left, I am a student in the School of Death, so when talking to Sabrina Greenstar the Death Shield is FREE. All the other spells, which are in different schools, will cost 1 Training Point to learn.