You can learn more spells outside of leveling up by looting Grimoires.
Once a Wizard acquires a new grimoire, simply place it in their inventory, and Right Click on the grimoire, as you would to see the stats on any other item. Any spells stored in the Grimoire which your Wizard does not know will have a small + icon on the top right corner. Clicking on this will give you the option of learning a new spell, at a cost of 100cp Per Level of the spell being learned.
The first such Grimoir that you're likely to find is on the eastern end of Magran's Fork, just south of Gilded Vale. You'll encounter a pair of Goldpact Paladins, accompanied by a wizard named Ludrana. They'll attack on sight, and after looting Ludrana's corpse, you'll have a new Grimoire to learn a few new spells from.
Alternately, if you're interested in learning a specific set of spells, and have gold to burn, you can hire a new Wizard adventurer at the Inn. Give this hireling all the spells you'd like your wizard to learn, and then steal his grimoire before kicking him out of the party.