The Wizard is one of the newest class additions to the Diablo game series, along with the witch doctor, monk, and demon hunter. It essentially replaces the sorceress that existed in Diablo II.
Leveling a wizard can be extremely time consuming if you don't properly prepare or use the right set of skills. Here are some of the best ways to ensure that you will level as fast as possible while playing a wizard in Diablo III.
First off, it's important to ensure that you do everything you reasonably can to get the best gear on your character for leveling. This doesn't mean that you need to seek out legendary gear but it does mean that you should check the auction house to get the best pieces you can afford as you level. Having good gear means that you'll do more damage and have more vitality; this is important and will increase the speed at which you can level. Other options for getting gear are checking out the vendors in town and using blacksmithing to create gear (you can also have a friend with blacksmithing do this for you).
Also, make sure that you have a ruby placed into the socket in your helm. A ruby in your helm will increase the amount of experience you gain while leveling and dramatically reduce your leveling time.
Finally, for your follower, be sure to choose a Templar so that he can heal you. This will provide you with the best survive-ability, which you will need to make it through Normal to Nightmare, onward through Hell and into Inferno.
While playing the wizard I've developed a build that is designed especially for leveling. It includes using the following skills: Magic Missiles, Arcane Orb, Frost Nova, Wave of Force, Familiar, and Magic Weapon.
For passive skills this build utilizes Glass Cannon, Astral Presence, and Power Hungry.
Remember that you won't get all of these skills right off the bat, so you'll need to be smart about it all and integrate them with the skills you currently have until you have all of the skills available to perfectly match the build.
If you are wondering what to expect when leveling a wizard, in terms of whether or not it will be slower to level than other classes, I can provide some insight since I have played all of the classes in game. If you take the time to get gear, socket your helm, pick the templar as your follower, use this build, and do your best to avoid taking loads of melee damage you will find that you can level as fast as or faster than the other classes in game.