The basic mechanical design is simple, but you need at least a model to copy it.
Basically is a horizontally 50 ohms coaxial cavity transmission line (with air dielectric), having a cut slot along its length.
A shunt-connected vertical stub (which is shorted at one end) is moving alongside the initial horizontal transmission line, and also having adjustable length (using a micrometer in your picture for accurate reading).
You can use only one stub, but double-stub tuners can get a PI configuration providing wider range of impedance matching.
Brand new devices like this are very expensive (up to $4000) but second hand you can find for $100, plus shipping. I think is worth to buy instead making one.