Most of the Spells listed under Alteration either helps the player through utility or direct armor rating spells. Your Alteration level is raised when you use a spell like Candlelight or Magelight, making it rather easy to level if you got the time to spend. Those playing Warriors may also find the Alteration tree usefull since it contains two perks that directly reduce the spell damage you take.
The way you learn new Alteration spells depends on how high your Alteration level is, At the start of the game every race can buy Novice spells. Afterwards you'll be able to buy better spells every 25 level in the Alteration tree (Apprentice, Adept, Expert, Master). However to learn the Master spells (Mass paralysis, Dragonhide) you'll have to complete a quest from Tolfdir at The College of Winterhold, once complete your rewarded with Dragonhide with the other for sale in his shop.