"Never run after your own hat - others will be delighted to do it. Why spoil their fun?" - Mark Twain
I love knitted hats at this time of year. This beanie can be used by men or women, and is a great way for beginners to practice the Fair Isle knitting technique. I made the one below for my brother last year - it is knitted in his college fraternity's colors, and has his initials and his frat letters in a ring above the hat band.
For a typical beanie knitting pattern, go here and follow the basic knitting directions, ignoring the part that instructs you to knit the colored band.
You can find a variety of resources on the web from which to learn about Fair Isle knitting. The key to doing it well is to keep the yarn "steeks" very loose along the wrong side of the knitting, so that the hat can stretch easily. Also, try not to get the yarn twisted as you knit.
To figure out how to knit the pattern you want, use graph paper to sketch the pattern over 9 rows. After knitting the hat band, start the Fair Isle rows. When you have finished the last row, cut and tie off the yarn used to make the design, and continue knitting in the hat's primary color, as per the pattern's instructions.