First find a piece of straitish knot freeish wood about 3 and a half inches wide (90 mm) or more and half an inch thick or more and about 14 inches long or more. I got mine from a section of a plank taken from a shipping palette. A longer plank will give a longer ukulele. I have made a 2 foot long one (which is a Tenor Ukulele) using a virtually identical method and a standard soprano as well.
You can see how they sound here
First is the sopranino tahitian style tuning (apologies for the fat fingers)
Second is a tenor Uke tahitian style tuning.
Third is a regular tuned soprano uke all made using roughly the same method.
Step 1: Mark out your Uke
The scale length here was going to be 20 cm but finished up being 22 cm,or around 8 and a half inches.
Step 2: Excavate out the back
It is much easier to do this with a router.
Even I was not perfect and had to glue a crack back together.