You'd probably want to run over to ask anthropologists.

More broadly, prior to the understanding of radiometric dating techniques things were typically aged within the confines of what we knew. If you have one arrow head manufactured with a very specific technique and a very specific design, and you find another one, you know that the two are most likely related. If you're excavating a site one painful millimeter at a time, and you find artifacts at one elevation, and then even more at a much deeper elevation, odds are that the deeper one is older.

And to be fair, even radiometric dating can give you a lot of wiggle room. Sometimes you really are dealing with something that's millions of years old and radiometric dating can give you an idea of it's age, give or take ten thousand years. Or in the case of Radium Strontium dating, it can tell you if something is billions of years old, give or take a few million years. Or something is old but not the right kind of old, because it either doesn't have the right isotopes to measure- potassium argon dating, carbon dating, etc- to be measured properly.

Archaeology is one of the more scientific disciplines under the umbrella of anthropology, but a good half the discipline is still methods and interpretation, which can very much be more of an art. Dating was fairly reliable, but only if you stayed within the confines of recorded history. You could reliably draw a line from, say, Socrates to the modern period because we knew he was alive, we knew when he died, we knew who his students were, and we know that at the end of this line of thought Alexander the Great goes on a tour of the Middle East and makes some Babylonians cry and eventually the Romans show up and decide that Greece looks like a cozy place ton conquer. On the other end of the spectrum we have lost works of people like Plato (Hermocrates), or Archimedes (On Sphere-Making) or Homer (Margites) or even some of Shakespear's work (Cardenio) which we often only know about because someone else references them in their writing.

Dating an object- or a person, or a place- without the perks of radiometric dating is often done much like navigating on a map. If you can plot it on a 'map' relative to an important date that is well established, you can establish, roughly, the age of something else.