Before saying anything further, though, we should mention that Miller Hats does a very good job of explaining what type of hat to wear here: http://millerhats.com/hatcare_index/hatfaces.html
We will attempt to offer a summary of some of the tips for wearing a hat here:
The main idea here is that the hat is like an extension of your head. Therefore, depending on the general shape of your head, you will want to balance certain features out by picking and choosing what type of hat to wear. Let’s see some examples:
Let’s say you have a short and full face as demonstrated in the picture below:
With this type of a face, you will want to wear a medium crown so that the hat does not look like it is squatting down your face. Also notice in the picture that when the hat band does not have the same color as the hat itself, the hat does not look as tall ( a good thing if you have a short and full face).
Now, let’s look at another example. Let’s say you have a long and slender face like the picture below:
In this case, you will want to wear a hat with a smaller crown so that the hat looks like it is a part of the face and does not make it look even more long. Furthermore, you want to avoid a small-width brim as that will make the hat look taller as well.
In short, you must take a look at your own facial features and see how you can balance or even emphasize certain features by using a hat. If you do want more information, you can check out the Miller Hats website.