So, "magic," traditionally, has meant several different things in folklore beyond just "a power you can weild to do stuff." So I think a great way to approach "folkloric" magic is to consider its origins. Why did people think some things were magic?
Here are some of my ideas, which are all closely related variants on a theme:
Superstition. Human brains are powerful pattern-recognition engines. Superstitions develop when your brain interprets coincidences as pattern (there's a cognitive bias in which people tend to remember and consider unusual events more than normal ones).
Magical Thinking. This is a psychological phenomenon in which people think two totally unconnected events or phenomena are related. Sometimes people mistake correlation for causation, and sometimes it's just more superstitions. People still beleive this today, from the "power of positive thinking" to athletes with lucky socks.
Sympathetic Magic. This is like the "noun form" of magical thinking; people associate the part with the whole. Homeopathy is a modern-day version. People think that acting upon a representative object will translate into changes on the actual object, like the classic voodoo doll, or scrying/enchanting someone by acting upon a bit of their hair or a drop of their blood.
Symbolic Reasoning. "The symbol is the referent," so if you manipulate the symbol, you can affect the referent. This is the more generalized version of sympathetic magic, as it can also encompass magic words, numerology, sacred geometry, etc. Language itself, and writing, were seen as magical in ancient times.
Narrative Reasoning. This is the idea that there is a "story" and things play out according to some plot. I think it's more prevalent in modern fiction (
Star Wars can be read this way particularly well -- the Force is the Plot, and Obi-Wan and Darth Vader are both Dangerously Genre-Savvy). But you can also find it in the more self-aware myths and fairy tales. This is related to the above ideas because plots and narrative structures are really just more patterns.
Unexplained. Magic, on some level, defies rational explanation. Comic for reference:
https://www.sciencecircle.org/wp-content/uploads/2020/02/S-Harris-Then-a-miracle-occurs.png . People still often shrug and say "it's magic" when they don't have a good explanation for something, and we have phrases like "voodoo economics" or the magic numbers in software. Clark's Law ("Any sufficiently advanced technology is indistinguishable from magic") isn't really about the power of advanced technology, it's about the inexplicability of advanced technology.
Hidden Laws. Putting this all together, I think the theme is that a belief in magic asserts that there are hidden laws governing the universe, and that these laws can be learned and utilized, but not (fully) understood. Humans crave reasons for things to happen, but often the universe is not forthcoming, so we just make stuff up.
But in a setting with folkloric magic, that made-up stuff should
actually work. I think this is what people are getting at when they talk about "rituals" in this thread. To me, it's not so much about casting spells without using spell slots, it's more about the practical knowledge of a supernatural world. E.g., sleep with an egg under your bed to ward off the Evil Eye. Or, if you want to go to the Feywild, visit the crossroads at midnight under a full moon and when a troupe of elven troubadors comes through, go with them. But before you go, pry a nail from your house; once in the Feywild, if you suspend the nail by a string over a bowl of water, it will swivel and point the way home, like a lodestone. Stuff like that.
If I were running a folkloric magic setting (and I might, very soon) I'd jam it full of twisted little laws that the players can exploit. I'd probably make some of them common knowledge, and for others, I might require knowledge checks. I'd love to make some random tables to help generate superstitious elements on the fly.
It's important to keep Sanderson's First Law in mind with this kind of change ("The ability of protagonists to use magic to solve their problems is directly correlated with how well magic is defined"). This is why the D&D spell system is so well-defined; it's meant to allow protagonists to use it to solve problems. Using folkloric magic, which is much more nebulous, should be risky and uncertain and have unexpected side-effects. Instead of solving the protagonists' problems, the magic simply swaps them for new problems which may be slight easier to solve and also slightly more interesting. E.g., instead of searching house-to-house for the fugitive, you can perform a spell to locate him, but this requires you to first gather some magical doodads and learn the fugitive's full name (a bit of mild investigation). Either way would take about the same game time and be about equally effective.