Step 1: Print the pattern from the pdf on the above website (you will need Acrobat Reader), or cut your own using my picture as a guideline for the shape (as always, you can click on a picture to see it larger--The center line on the pattern piece measures 6.5"). Cut out 6 of these from the fabric you want for the top of the hat, 6 for the inside, and if you want to give it more structure, 6 from interfacing. I'm going to use the yellow floral fabric for the outside of the hat, and the red polka-dot for the inside. You can see here a pink floral one I've already finished.
Step 2: Piece together your sections in groups of 3. Here I am working on the red polka-dot lining. I sewed 3 of the 6 sections together, then sewed the other 3 sections together so that I end up with two matching halves (pictured here). Do the same for the other fabric and the interfacing if you are using it.
Sew the two matching halves together. Hopefully your seams will be lined up on the top, but if not, it isn't a big deal. The pink hat I made wasn't matched up very good, but with a busy fabric you can't even tell anyways :-)
Optional Step 3.5: If you would like to put a chin strap in, this is where to do it. Line up your strap (I just used a piece of elastic I measured on my daughter) between the two halves of your lining fabric and sew it in. The hat will no longer be reversible, so it just depends on what you want. You could also sew on a chin strap later (which is what I did with the pink hat I made because I didn't think about it until I after I finished it).
Step 4: Stack your layers together. It doesn't matter which fabric is on top because you can flip the hat later for whichever fabric you want on top. The only thing you must make sure you do is have your two fabric layers together (don't put the interfacing between them) and that the fabric is laying right-sides together. If you look at this picture closely you'll see that the right side of the red is facing down, and the right side of the yellow is facing up.
Line up your seams and sew the layers together around the outside, leaving an approximately 2" gap somewhere in which to turn the hat right-side out. This is a good place to mention the importance of cutting your pieces out the same size and using the same seam allowance so that your seams will line up nicely.
Step 6: Once the hat is flipped right-side out, top-stitch around the brim to close the gap you left in step 5 and make a nice clean edge all the way around. Now just put it on your kid and enjoy!