Yer a Wizzard, Rincewind
Our tireless researchers have finally cracked the ancient techniques of spellcasting!
To begin, you'll first need a wand, of course -- head to Ollivander's on Spawn Ranch to try finding the type of wand you're destined for! You can also be sorted into your house and buy some basic spellbooks here.
From the Ollivander's 2 Wiki:
Spells are cast by first speaking the spell incantation in normal chat with a wand in your hand. You must learn the spell from a book! Simply knowing the words to speak is not sufficient. These spell incantations do not take capitalization into account. After speaking the incantation, left clicking with the wand still in your hand will cast the spell, which takes the form of a rapidly moving ball of particle effects. Hitting living entities requires aiming for their eyes.
The more times you have cast a spell, the more powerful it will become. If you have over 100 (one hundred) casts of a spell, then the spell is saved in your memory for nonverbal casting. Simply left click again and you can cast the spell as many times as you want. You can scroll forward and backwards through the spells you have mastered nonverbally by holding your wand in your left (off) hand and right- or left-clicking. Once you've selected the spell, you can cast it with your wand in your right (primary) hand as normal without saying the incantation.
[NOTE: spells like "reparo" which target an item cannot be cast on the item in your inventory! The item MUST be dropped on the ground to be targeted!]