Aren't those owls the cutest thing? They were part of Jess's birthday present since I've been brainwashing her about the joys of knitting. (The other part was of course yarn.)
These are a very do-able project. First start out with a dowel of the desired thickness. Cut two pieces to the desired length, I chose 12 inches. If you don't have any sort of saw handy it is possible to work at it slowly with a pair or scissors you aren't fond of but I would only recommend that for thinner dowels. To make the point. carefully use a good pencil sharpener. This will give you a place to start. Sand like crazy to smooth the tip out and gently round the point. Sand the body and top end well, knitting needles need to be very smooth!
There are many ways to decorate them when you are done. I used Sharpie's to make patterns and sprayed a sealer but you could stain them or even leaving them plain looks quite nice. I used contact cement to glue some ceramic beads to the tops. (The skinny pair needed to be re-glued so beware of using too big of a topper.) People often make pretty tops out of polymer clay as well but I have never tried that method.
I have also made double pointed needles this way. They have lasted me several years and are used often. I am finding that the points of the larger set are blunting a bit because the dowels I used were a fairly soft wood. I also didn't seal them in any way. It's fairly minor though. I just mentioned it as a reminder that anything you could cut with scissors wasn't going to last forever so pick a better quality dowel if you're worried.