Normally you’d have a functionality QA dept handling that sort of thing. There’s some automation and human operators / analysts. Assuming you’re asking from the Indie-dev point of view, though 
As a general rule of thumb, you run it on multiple hardware configurations / game settings and collect data.
In order to get somewhat consistent results, you’d write an AI bot that’d fake-play the game and perform similar actions as players would. Or think along the lines of a built-in benchmark with a camera fly-through. A small automation tool like that would help a lot - ideally, it’d would gather, display and save the pertinent data
Once you have the data, you can draw conclusions. There are no set rules or metrics; I guess 1080p / 30 fps on Lowest settings should be the entry point. You could simulate performance to an extent by disabling CPU cores on your super-duper-dev-rig and gimping the GPU via underclocking (if you know what you’re doing). Eject a RAM stick.
You could consider distributing a limited demo version to friends / family, ask them to run the Benchmark you created on their machines and send the results for Low / Med / High back.
This should give you a rough idea of how the game performs across more configurations.
Some serious reading: