I don't know how others would do it, but personally, I would start by identifying the existing pump by size, style, and dimensions. Is it a two bolt mount? What size flange? Most two bolt pumps would be A flange or B flange. A flange has 3 1/4" pilot bore with 4 3/16" bolt spacing. B flange has 4" bore with 5 3/4" bolt spacing. Is your pump one of those? Maybe, maybe not. Then comes shaft size/style. Round shaft with straight cut keyway or maybe a splined shaft? Then inlet/outlet port size/style. ORB fittings, pipe thread, bolt on flange type, etc. Pump volume requirement and of course shaft rotation direction.
Plenty of stuff out there to choose from if you know what you're looking for. Sometimes the pumps can be identified by manufacturer and have certain I.D. numbers stamped into the mounting flange somewhere. If you find that it might help.