When I was in elementary school my family owned a coffee grinder that had taped to it a piece of paper indicating how many seconds I should hold down the lid for various types of coffees. It was my first real window into the world of coffee grinding. For such a simple process - take beans, add water, get coffee - there are so many different points at which altering the process ever so slightly would actually make a world of difference. Grinding is one such step.
To remember how finely you should make your coffee, simply keep in mind one key fact: the finer the grind, the more you increase the extraction rate of the coffee (combining both time, since the grind slows down the flow of the water, as well as the surface area, by increasing the exposure of the coffee to the water). Everyone's exact favorite levels will differ from person to person, but it is safe to say that the faster the process of making the coffee, the finer you should grind it. As such, coffees like Turkish Coffee (which can be brewed in less than 45 seconds) or Espresso should have very fine grinds, whereas Cold Brew (taking upwards of 18+ hours) has the coarsest.
While the type of grinder you have will generally affect how consistent the grind is, I am of the heretical opinion that most grinders will probably serve the average person well for a wide variety of purposes.
Now that you've read this short intro, go out and grind!