The main ingredients are herbs and wood, you can get them either by gathering, planting or buying from auction house. There's also a couple other ingredients, one can be bought from a cooking supply merchant in every town, the other is an activate rune, which you only need if you use recipes higher than level 11. Activate runes drop often, and they can be bought cheap at auction.
There's two types of recipes: White, which you buy from the instructors, and green, which are dropped by monsters. To learn a white recipe, just level cooking up and buy the recipe, to learn a green recipe, right click on the item in your inventory and, boom.
You can learn green recipes even if your skill level isn't high enough. But you can't make them until your skill gets that high. Green recipes, BTW, require much more ingredients, including an uncommon herb, but they are more powerful though.
You can review your recipe list by hitting K, then selecting cooking from the general skill.
