Keep using the spells you have (see the tab that has a picture of a little book on it to see the spells you can cast). To cast spells you need to have runes, which you can buy (or make, after completing the Rune Mysteries quest). As you use spells, you gain experience. Once you gain enough experience to get to the next level, you will get a message saying something like: You are now Magic Level ! or whatever level you become. Keep casting spells and getting experience. The highest level you can get to is, I think, Level 99.