Well, I'll try a written description for now: let me know if it is too hard to follow.
Pull the drill holder out of its slot by the knurled knob, unscrew the knob, pick out the correct collet for the drill in hand, pop it down the drill holder, and replace the clamping knob. Put your drill down the hole to project a little from the bottom of the holder and clamp very lightly.
The holder is drilled through 3/32" and is counterbored 5/32" for the collets. The two diameters are joined by a 30° included taper, leaving only 1/32" length of the smaller diameter at the very bottom. The taper is cut with a purpose made D-bit reamer. The collets have a matching taper at the nose. This provides support for tiny drills as close as possible to the diamond plate.
Now, looking at the tip of the drill, end on, align the cutting edges parallel with the long sides of the rectangular section holder and screw the knob tight. Magnification is generally needed. Drop the whole lot down the 25° slot in the body.
The slot is cut at an angle across the sloping face of the block to provide the required 59° point angle. Because of the compound angles the rectangular slot emerges from the top face of the block as a parallelogram.
Take the block for a few strokes up and down its guide rails while applying light downward pressure on the top of the knob to press the drill against the abrasive. Pull the holder out to check progress. Once one side is ground, turn the holder 180° and do the other. Centrality of the point is gauged by eye.
Finally flip the block end-for-end and use the 10° raked slot to make the lands just behind the cutting edges. This may take only a short rub. All four ground facets should meet at a point.
When a strip of diamond is worn out, slacken the rails and slide the plate along a bit.