This is a short guide that will provide a general framework for artifact hunting so you can know you're on the right track, without spoiling everything. If you do want spoilers, check out one of the other steam guides on artifacts or head over to the excellent wiki: https://riskofrain2.gamepedia.com/Risk_of_Rain_2_Wiki .

On the 5th stage, Sky Meadow, there is a very conspicuous "secret" area. Once you're there, the visual clues as to what you need to do are mostly straightforward. If you think you've done everything correctly but nothing's happening you may still need to submit your choice using the computer behind you. Once you've gone through the portal to the hidden realm, complete the trial to unlock your first artifact!

Now you know basically what you need to do: find the remaining "objects of interest" that will let you make another correct choice at that same "secret" area in Sky Meadow. The one prominently displayed in the "secret" area was easy to find; the others will not be so simple.

A quick look at the logbook will tell you there are 16 trials, and therefore 16 artifacts, in the game (as of April 2020). The logbook will also tell you there are 15 environments in the game. Because these two numbers are close but not equivalent, I think we are supposed to assume that in general there is a one-to-one correspondence between artifacts and stages, but that there are also exceptions to this rule. This assumption is correct.

In the next section I will outline the exceptions a little more explicitly. If this is enough information for you, stop reading the guide and go explore. If you want just a little more guidance, read on.

It turns out, in fact, that there are 16 "objects of interest" hidden throughout the 15 environments, with Abandoned Aqueduct containing two and each other stage containing one. Keep in mind, though, that some stages have multiple layouts: "objects of interest" may only appear in one specific layout.

However, these will only add up to 14 artifacts (it will make sense once you find them). It is difficult to provide a hint for the general locations of the two non-stage "objects of interest" without giving most everything away, other than what has already been said: they are somewhere in the game but not in any of the environments. But if you really want to know generally where these two are, there is one in the logbook and the other is in the settings menu.

Thanks for reading! I may add more specific hints for each stage later, if requested. If I made any errors in this guide, please let me know.