Water, Water Everywhere
I don't know that there's anything special in itself about a dowsing stick. So to celebrate Learn to Use a Dowsing Stick Day, just find a forked stick that's a couple of feet long and start practicing your dowsing with it.
If you already know how to dowse, it is acceptable to celebrate the day by just doing the dowsing you already know how to do.
The real trick, of course, is proving that you've dowsed correctly by showing someone the water buried underground in the area your dowsing stick is pointing to.
Water in pipes, under or above ground, don't count.
Neither does water in public or private pools or baths.
The water must be initial unviewable or dowsing wouldn't be a thing.
If you're not sure how to dowse, check YouTube or possibly reruns of The Andy Griffith Show for acceptable methods.
You'll know you're really good at dowsing when you can do it in the desert.