You can get enchanters elixir from random loot or from the store. It's fairly high level item and you won't find it in early game. It's pretty rare.
You need blue butterfly wing, hagraven claw, snowberry, or spriggan sap to make enchanting potion. http://www.uesp.net/wiki/Skyrim:Alchemy_Effects
You can make stronger potions by having better alchemy skill, taking perks in the alchemy skill tree, and wearing fortify alchemy enchanted clothes.
There is no fortify enchanting spell.