Fire powers are generally used for tanking, although there is a spec which will help you to do a lot of damage quickly. The two specs in fire are Immolation and Ignition. Immolation does damage and helps you to stay safe by providing you with tanking specifications, as well as increase your survivability. Most spells come from the fact that you are engulfed in flame. Alternately, ignition is about setting others on fire and using the firepower to your advantage. This is a higher DPS spec (damage per second) and used for that purpose solely.
The two specs in ice are cryogenics and storm powers. Cryogenics is also a tanking spec and will help you to reduce damage, heal, and help you stay alive. Storm deals with helping you attack faster whether you are melee or a ranged attacker, and will drastically increase the chance that you defeat your opponents. Using the abilities that are inherent in the Storm Powers will help to keep them far, close, or next to you, giving you a lot of control over your enemies.
Mental powers are generally for casters, which will help you if you are interested in using magic to defeat your opponents. Telekinesis is the first specialization and means you are a wizard-like character, using the magical powers around to defeat your enemies. Illusion is all about supporting your teammates and will grant you a lot of control.
Nature is all about healing your friends. There are two specs, again, and these are Shapeshifting and Plants. Shapeshifting will actually allow you to tank and DPS because you can literally change the form of your character, becoming either a bear or a wolf. You can tank and do damage with these two distinct abilities. As a Plant Specialist you will be healing your friends primarily.
Using a step by step guide for a ton more detailed information, and more importantly, advice that will help you to master the game.
Here's the best guide that you can use to master the game and begin to do well. It's really the best one of its kind because it walks you through the quests and will get you to level 30 very rapidly, and from there will help you to get good gear and raid.