To cut internal threads a hole is drilled. Then a tool bit, called tap, cuts the threads. The tap is quite similar to a sharp-edged screw. What kind of tap that is suitable for each thread depends on the material of the workpiece, the thread's diameter and depth, and the specific kind of thread.
Most workshops do threading with taps and dies. There are workshops that focus on threading, often in large volumes or with high precision.
See thread cutting for more information.