I like to use a garlic press for this sort of thing. You drop a whole clove or two in the device, squeeze, and you get a perfectly smooth garlic paste. The one downside is that it can be quite a pain to clean.
There is also the Microplane (I'm not sure if there is a generic name for this type of rasp-style grater). Although I see it as ideally suited for hard cheeses and citrus zests, it generally does a fine job on garlic too. It means that you don't have to have on extra specialized tool. The downsides are again the cleaning (though not as bad as the press) and the likelihood of nicking your finger as you get down to the last bit of garlic.
Here's a simple method that I use when I really don't feel like getting one more device out (or dirty). Lay the garlic clove on a cutting board and lay the side of a chef's knife over top of it. Then smack it with the heel of your hand hard enough until you feel the garlic yield under the pressure. The garlic has been "crushed" but is still holding together. If you dice it very finely at this point, it will have a much better "crushed" texture than if you do not smack it first. I do find that the other methods yield a superior result, but this method is often more than sufficient.