Generally, correspondences are used as a sort of cheat sheet. It groups materials into categories so when we're looking to figure out what to put into a spell, we've got this pool of ingredients to choose from based on the category we might put the spell into. Correspondences were historically tied to ancient healing modalities. Different ailments and part of the body were said to correspond to different planetary energies and the "humors", different body fluids, to the elements. Herbs & etc. were also given correspondences with the idea that if you didn't have enough of a certain energy, you could add it through herbs (& ect) to balance the body's energy, or if you had too much, you could add the opposing energy to reduce it, etc. As medicine separated from magic, it left this sort of system behind and magic expanded on and applied it more generally till we get what we have today. If you learn how correspondences work, you will find that you will eventually be able to sort them out yourself without looking at a table. And as you go along, you'll find you have go-to stones and herbs and things just become simpler. Alchemy-works.com has some good information about how plants are grouped into correspondences, you might want to start there.
That all being said, instinct is one of a Witch's most valuable tools. And witches improvise. Witchcraft isn't about finding just the right ingredient, it's about doing what needs to be done when it needs to be done using the materials at hand.
