While coffee shops will almost always offer to grind the beans you purchase for free, this doesn't mean it's a good deal. Once ground, coffee should be consumed as fast as possible. Roasted coffee loses much of it's luster after being exposed to the air. Grinding a bean only means there is more surface area exposed, so the beans will lose their flavor much more quickly. (Any good coffee shop will be aware of this.) Some ultra-automated home espresso machines actually grind the beans for you a minute before the espresso is made. Of course, purchasing a decent home stand-alone grinder won't bust your budget, unless you're homeless and thus have little use for appliances anyway.
How fine to grind
So how fine should your coffee be ground? While there is an infinite level of fineness possible (almost) there are essentially three types of grinds you'll want to achieve for different purposes. Let's examine these, shall we?
Drip grind: This grind can be anywhere from very coarse to somewhat fine. Drip coffee will be quite a bit stronger with a finer grind, but it should be less fine than espresso. If the grind is too fine, you'll end up with some pretty "sandy" coffee. Major brands of drip coffee seem to be grated into strips for some reason. Major brand coffee = big yuck.
Espresso grind: This is a very fine grind, but it shouldn't be so fine that it goes through your filter! It should look like fine sand. The increased surface area unlocks much of the flavor of good coffee.
Turkish grind: This is an extremely fine grind. In fact, it's so fine that it's powder. Turkish coffee is made by mixing powdered coffee with boiling water. This process may look like the makings of instant coffee to the unknowledgeable observer, but the joke is on him — Turkish coffee is not horrible and disgusting (if made properly.) On the other hand, since you will be consuming bits of burned carbon, you should realize that drinking Turkish coffee on a regular basis puts you at risk for cancer. But you're going to die anyway, right? Might as well have some yummy Turkish coffee before you're six feet under. Yes, that's your happy thought for the day.