The Wizard is a brilliant arcane warrior that weaves the magic of the elements into devastating spells that do massive amounts of damage in a short period of time. They also have powerful area of effect abilities that can transform small armies into piles of charred meat. They use primarily fire and ice, wear robes and wield a staff or dagger. They're an excellent class for players who mainly want to just put out a lot of damage as a caster. Their low survivability and lack of crowd control utility makes them primarily a group class, although they can solo if the player is dedicated enough to it. They shine when they have a good tank to soak up lots of damage and threat for them, so that they can unleash their magical energy. It helps to make friends with a good tank so you have an idea of just how much damage you can do without ending up a greasy stain on the floor from enraging your foes.
Their most important statistic is intelligence, as it gives them a higher power pool. Wizards are greatly limited by the amount of power they have available, as many of their abilities drain a lot of it. When a wizard is out of power, they're out of tricks, and can only do minor damage. As such, it's important to be conscious of the efficiency of your spells, particularly when you are facing an encounter with many monsters. It's often best to begin a fight with your damage over time spells like Cold Whorl, as it also reduces their resistance to cold. It helps to have some knowledge of the monsters that you're fighting as well, as different monsters have different resistances to various elemental types. Use the right element for the job, and you'll do more damage for less power. Once the tank has the creature's attention, then you can start following up with your heavy direct damage spells to finish them off quickly. Of course, more competent tanks will enable you to start bringing out your heavy direct damage that much faster.
Wizards can also buff their party with Amplify, which increases the group's elemental resistance and their power pool. Painful Meditation allows the Wizard to convert some of their health into power - perfect for long fights in which you've run out of power. Buffs like Accord can be used on an ally to restore some of their power when they're hit in combat. Similarly, Intromission damages a Wizard and transfers that into some power for an ally, which can be quite useful for when a healer runs out of mana.