I used Homespun Tudor, Black, and Colonial, 1 over 2 e-wrap stitch, using the traditional method to make the hat and attaching the brim while knitting.
The second hat I made based on the pattern for the garrison hat I knit before (http://loomdude.blogspot.com/2010/05/for-all-veterans.html ), all with 1 over 2 e-wrap stitch:
Instead of making the hat flat on top, I made it round like a regular hat. I simply knit the body of the hat first, then knit the brim separately. I positioned the brim the way I wanted it to look on the hat, fastened it to the hat using yarn needles (though you could probably used safety pins or other knitting needles) and then carefully sewed it the bottom of the brim to the bottom of the hat using a yarn needle and Homespun black. Then I sewed a row of Homespun Shaker around the top edge of the hat brim, attaching the brim to the hat as I sewed, and removing the yarn needles I had placed for positioning. As you can see, I wasn't fanatical about the line I made with the Shaker yarn being perfectly straight. After all, I knit it a little loose so it could stretch when the hat was worn; otherwise it would probably feel tight around the head in that area.
Finally, I made another hat based on a hat that I knit for myself in 2009. I used Hometown USA San Diego Navy and another dark blue yarn I had that was gauge 4. I double stranded the yarn and knit 1 over 1 e-wrap stitches, attaching the brim during the process. The brim on my hat was much wider (about 3"); this brim is about 1.5"-2".
Unless you look closely you will not see the variation in color between the two yarns I used. I decided to knit it this way because when I only used the San Diego Navy yarn and knit 1 over 1, it left gaps which I knew the wind would easily get through. Using the two gauges of yarn together double stranded helped solve this problem, though on an extremely windy day you will still feel the air blowing through momentarily. I've used this hat outdoors and it is heavy enough to make me sweat if I'm shovelling snow or playing with my daughter, so I usually only wear it when it's below 40 degrees.