Every time you gain a level you will automatically receive one talent point. Every five levels you will gain one extra talent point. The talent points can then be spent in the talent tree to learn new spells and upgrade existing ones. The talent tree can be accessed in the talent tree tab of your Talents window.
When you learn the first rank of a spell it will only cost one talent point. However, when you upgrade a spell to the second rank, it will cost two talent points and upgrading a spell to the third rank will cost three talent points. In total, it will cost six talent points to learn a rank three spell in the talent tree.
Additionally, some spells in the talent tree require a minimum amount of talent points to be spent before you can learn them. Because of this, certain spells can only be learned at higher levels.