Represent your school!! I just released the Team Colors Earflap hat on Etsy and Ravelry.
It uses half-double crochet and single crochet for an easy work-up. Note that this pattern is for the base hat, NOT for the embroidery representing any particular team. So, this blog post describes how I added my team embroidery so that you can get ideas on how you can customize your hat.
First, I found an image that I wanted to use and printed it out. I reduced the size by making a copy and reducing it by using the copier setting (old school style). Next, I used a thin, translucent paper to trace the image. Actually, I used parchment paper, like the kind for cooking since I don't have fancy tracing paper or that special temporary fabric used for embroidery.
Let me take a time out to note that embroidering on crochet is an imperfect art. The spaces between stitches can distort stitches. I found that making a good image worked better by only embroidering the outline rather than filling it in. For the embroidery masters out there, please chime in with tips. My guess is sewing some fabric to the back of the forehead flap may make an improved embroidery "canvas".
Back to the instructions... I cut out my traced image (keeping some border space) and placed it on top of the forehead flap where I wanted the final image to go and temporarily pinned it there. Next, I used back stitch to embroider the outline of my design.
Finally, I carefully removed the tracing (parchment in my case) paper in small bits to ensure that I didn't distort any of the stitches. I tested filling in the outline at this point but was not successful in producing something that I liked, so I kept it as an outline.
I'd love to see your own results or hear your tips!