Basically grits are corn, ground from hominy which is the inside part of a corn kernal. Dry that and grind it just right and you have grits. These days they make three varieties of grits: traditional slow cook, quick cook, and instant. Instant may be most convenient, but they don't taste nearly as good as the other two types. Unless you don't have full kitchen facilities, such as when on a trip or in a dorm room, I would stay away from instant grits.
There really isn't much, if any, difference in the taste of slow cook and quick cook grits. Slow cook takes 20 minutes of boiling to cook, while quick cook only takes 5 minutes. Personally, I always buy the quick cook but if you want the old timey traditional experience try the slow cook.
Most people who have never had grits don't have a clue how to eat them. Many assume you would put milk and sugar on them like you would oatmeal or cream of wheat, but that is totally wrong. Grits have a very "corny" taste, sort of like corn chips, which doesn't go well with sweet toppings. Grits are meant to be served as a savory hot dish. You can top them with butter or add in other things like bacon or cheese. Here is the basic recipe for a single serving of quick cook grits:
1 cup water
1/4 cup grits
dash of salt
Bring water to a boil and add grits and salt. Reduce heat and simmer for 5 minutes. Remove from heat, cover, and let stand for 2 minutes before. Serve in a bowl with a pat of butter on top.
For cheese grits, add 1/4 cup of grated cheese (cheddar or your favorite type). For bacon grits, crumble 2 slices of cooked bacon into the bowl and stir. Other tasty additions are ham and scrambled eggs.
Remember, in the South grits aren't just for breakfast. Cheese grits are often served as a side dish for dinner.