Making a kendama in wood involves a series of simple turns on a lathe; however, making the cups requires using a jam chuck and scraping to an exact diameter so that the ball fits exactly into the cups. Some experience with wood turning is required.
The other tricky part of the process is scraping the ball to the correct smoothness and size. An armrest and angled scraper are required in order to achieve a nicely spherical ball that can have the necessary hole drilled dead centre to allow it to be caught on the "sword" of the toy. Careful measurements with both a straight line and compasses are necessary throughout the process in order to ensure that all of the parts are exactly in proportion to one another.
A kendama is not the sort of project that a complete beginner at wood turning can achieve perfectly the first time due to the precise measurements required. However, for craftspeople with existing woodturning skills, there are detailed instructional videos available that can help explain the complexities of the process. One of the best is provided by the Woodworkers' Journal, and it is available for free on YouTube. Other wooden toy demonstrations are also available on the Woodworkers' Journal's own website.