Note from the Creator: Magic in the Weird is based on belief. When I constructed The Weird setting I was thinking about the human collective consciousness theory and considering a fictions where humans may unknowingly be constructing mutual reality through belief systems. The general idea is that if a person has strong enough belief, or there are enough people with the same belief, an impossibility becomes a reality. For example, if enough people believe in Angels, then, POOF! Angels are real.
The idea behind magic is that if you believe in your ability to cast magic, then you become able to cast magic. Likewise if you believe you are immortal, you become immortal. Humans unknowingly ruin their opportunity to fly by telling children they can not fly. Up until someone plants the seed of doubt, there is nothing a human can not do.
Of course, there are some things to ingrained in human culture that they would be nearly impossible to alter at this point - like feeling pain, needing food/sleep/temperatures. But there are ways to remove oneself from the confines of systematic restriction. Those methods are known as Magic.
One of the ways to avoid the confines of accepted reality is to circumvent them with rationale. If you can justify how what you are doing works, you can believe that it is normal. The traditions of magic are passed down through the generations and because the people practicing them believe it worked in the past, the ritual makes the magic easier to use. So if your great-great-grandmother used to walk in a counter-clockwise circle chanting a prayer to Hecate asking for a good harvest and it worked, then you can perform the same ritual in the same way saying the same words and your belief is strengthened. However, this means there are limits built into ritual magic. So if you believe a ritual can only be cast under a full moon, then the ritual can only be cast under a full moon. And the more times it is repeated as needing a full moon, the more tightly bound it is to the full moon.
A note regarding religions: One of the more contentious views of magic is that religion is a form of ritual magic.
Perception & Madness
One can overcome barriers of culture/society by altering perception through consuming mind altering drugs, etc, or becoming so departed from cultural touch stones that one is considered insane/mad/crazy/whatever.
The big downside of this method is that no matter how much you believe you are summoning a fireball, if the person you are directing it towards does not believe in equal measure, then they will not be affected.
For example, hypnosis works best if the person receiving it believes in the power of hypnosis. The same can be said of most magical abilities. Believers are more susceptible to being harmed/helped by the magic because they are more inclined to believe it and therefore manifest the results.
There is some latitude for plants and animals - they are more easily influenced by human belief.
An item can be imbued with magic through ritual or personal belief. Artifacts are one of the few ways to overcome the blocks of others' beliefs. When an item is enchanted to make the wearer more lucky, it doesn't matter if the wearer believes in luck or magic - because the crafter embed their belief in the item, the item outputs that belief until it either runs out of power, or is disenchanted. This is why magical items can be seen through magical means; they are always emitting magic. It is notable, however, that active disbelief can overcome an artifact - it's just passive disbelief that is negated by the enchanting process.