Choosing Your Class - Be sure to decide which class you want to level as your main once Diablo 3 is released. This will allow you to start leveling a single character instead of trying all of them out before deciding which one will be your main. If you were not lucky enough to get into the Diablo 3 beta to test out the different classes, you can watch videos and use skill calculators to decide which class fits your gaming style. Each of the classes in Diablo 3 have different play styles and resource systems. Learn more about the different classes before you decide which one to level up.
Group Leveling - The difficulty of enemies in Diablo 3 will scale based on the amount of players in each game. This does not mean that leveling up with groups is harder. Yes, the enemies will have more health and do more damage, but your group will have access to more buffs and abilities with multiple classes in the same game. Leveling up with a group is faster and makes the game much more interesting. You will not have to worry about sharing loot because each player will receive their own loot from enemies and bosses.
Gearing Up - Be sure to upgrade your gear as often as possible. There will be two different types of auction houses in Diablo 3, the Real Money Auction House (RMAH) and the gold based auction house. If you do not find upgrades for your class within a few levels, you can always search these auction houses to find better items. To progress through Diablo 3, you will need to make sure you have the best possible gear for your level. If you are purchasing items from the auction house, try to avoid items with + magic find or + gold drops because you will most likely be able to find better items with damage increase or + experience gain to help you progress through the game.
Combos - Diablo 3 has a combo system that gives you bonus experience for killing multiple enemies with one attack, multiple enemies in a row, destroying the environment, killing enemies with the environment and more. Take advantage of these combo bonuses as often as possible for free experience. You will find yourself earning these experience bonuses without even trying just playing through the game. The bigger the combo, the more bonus experience you will earn.
There are plenty of other ways to quickly level up in Diablo 3. You will find shrines in the game that will give bonus stats for a short period like experience gain, attack speed, defense, ect. The game is still in beta for now but will hopefully be released to the public soon. Reaching the level cap as fast as possible will give you access to the end game content in Diablo 3. Once Diablo 3 is released, look for class builds and videos that will help you quickly and easily level each specific class in Diablo 3.