Spells are taught at Hogwarts, but it is not allowed to use them out of the school until 7º grade.
In order to use them you will need a wand. Ollivander who is the best wandmaker on Diagon Alley affirms «the wand chooses the wizard», then we can not help you so much with this matter. But we can remind you all the spells you find in this saga written by J.K Rowling.