Too bad I can't pick up any silphium or liquamen at the grocery store. Silphium is thought to be extinct and the exact taste and method for producing liquamen is still debated -- though we know it was some sort of fish sauce.
Plus garums are making a comeback and are already quietly being produced and used in some high end kitchens, based on work published by noma, using koji proteases to speed up the process. You can't quite buy them at the grocery store, and historical authenticity to roman recipes isn't the goal of anyone I know. But there is garum out there if you really really want it.
The recipe probably wasn't set down in stone. Which was of course one of the ways to publish information at the time. But mostly people just copied what other people were doing at the time. There weren't many recipe books/scrolls or literate cooks even. And it sounds like the process of making garum basically involved a lot of rotting fish guts so that doesn't strike me as something as a likely career choice for somebody with an actual education at the time.
So, basically the recipe would have gone something like: take whatever off cuts of fish, fish guts, etc. you have, add salt, and let it do its thing for some time. You get different results based on what fish you use, whatever else you might toss in (herbs, spices, etc), how long you let things ferment, etc. Probably all those variants would have been considered garum. Probably a lot of trial and error involved to get that right. That's also more or less how Asian fish sauces work.
Lots of seemingly minor details can make a big difference in cooking. From the Asian sauces for example I know it even makes a difference what fish species is used. It's possible that there are fish sauces out on the market that are similar or even essentially the same as variants that were used in Ancient Rome but we don't know this.
Maybe that's why we prefer to refer to the sauce as "garum" (although it's still in doubt whether garum and liquamen are actually the same sauce)...