I have a wand, somewhere...
Wood: hazel.
I used a series of chizzles and a hammer. Proper carving tools, then sanded it all down. In all honesty I still have to do some work on it.
Good peice of advice, don't start with a peice of wood that's too thick, it'll take days rather than hours. And a hazel wand will be white (naturally). I suppose you can paint it if you really want to