Physically, what is and how to, make an anti pad?
This is a case of a lot of ado about nothing, almost. Ott's style is unfortunately overly verbose at times, and the drawings are, frankly, atrociously confusing. An anti-pad is simply the hole in the plane, and is already there in any sane CAD. The only question is what size does the hole need to be, other than due to board manufacturability concerns.

First of all, you must calculate the skin depth for your signal, and then decide if skin effects play a role in the propagation of that signal's return current on the plane of a given thickness.

If they do, then the cylindrical surface of the hole in the plane is where the return signal flows, due to skin effect. You may wish to make the hole (the anti-pad) larger than the default, to lower the resistance and perhaps also inductance seen by the return signal.