The technical answer to your question is that a loop, probably of leather was tied around the two figures at the top of the clamp to act as a hinge.
The open bit was then placed around the penis so that the straight 'arms' went either side of the scrotum.
The 'handles' were closed and secured by placing a further tie between the projections. This would have been done as tightly as possible so that the 'neck' of the scrotum was severely compressed.
One the clamp was fixed in place it virtually cut off the blood circulation to the lower part of the scrotum and the testicles contained therein. All that was left was to run a razor along the underside of the clamp and, voila, one eunuch with the minimum of bleeding.
Of course, it is unlikely that the 'patient' was given any form of pain killer, so OUCH .