Grits is the Southern USAian term for a hot, ground hominy (big, white maize) cereal.  In other places, it's called white polenta, or white corn semolina.  There is also polenta made with yellow corn, wheat semolina a.k.a. "cream of wheat", ground rice, and a sort of ground pasta that is just a step finer than cous-cous, called solet. 
There are quick versions of maize semolina with directions on the package.  Here are the directions for cooking the non-quick version from white or yellow corn meal, for a family of four: 

   1.Put  5 cups of water, 2 teaspoons of salt (or more to taste) and a tablespoon of margerine, butter, or rendered fat in a saucepan or pot, and bring to a strong, rolling boil, on high heat. 
   2.Slowly pour in 1 cup of corn meal, while stirring. 
   3.Keep stirring until it takes on a creamy texture. 
   4.Turn the heat down to low, cover, and let boil for 20 minutes, coming back to stir it occasionally.  Be careful when you open the pot!  The boiling is explosive, and those bubbles pop pretty high. 
   5.After 20 minutes, it should be about done, but you can leave it on the burner for another 10 or 15 minutes on low, if you're still cooking other things. 
   6.Now, whatever else you do depends on your style... 

Grits can be... 
Baked: 

     Put the cooked grits into a well greased casserole dish, and spread garlic butter, or sprinkle cheese or brown sugar over them, and bake at 200 degrees, Celsius, until slightly browned on top.  Remove from the oven, and let the pie set for 5 minutes before serving.

Fried: 

     Pour the cooked grits into a greased or oiled, straight-sided container, and let cool throroughly.  Pop the grits out of the container, and cut into 2 cm. slices, and then fry in a skillet with butter, margerine, or oil.  Brown on both sides, and serve hot.

Served as a porridge: 

     Pour the grits into small bowls, and let set until cooled.  Then turn the cold grits out onto a plate, and serve with a sauce and meat to be eaten with the hands.  This way comes from Africa..