This is my very rough back of the napkin explanation but I’ll give it a try.
There are 3 aspects of the world. The physical, the spiritual and the cognitive.
The one thing all of the magic systems have in common is that the different shards affect how these different realms are used to affect others. Mainly through investiture (the spiritual potential energy if you will) to affect the physical, cognitive and spiritual realms.
In Roshar, for example. Investiture allows some to specify intent into the cognitive realm. Where the mental perceptions of things exist and have a kind of will over time. And when those are convinced to change it impacts the physical realm. The energy source allowing that intent to be work is Stormlight.
While in Scadrial (from Mistborn) there are actually multiple magic systems. One of which allows consumption of some aspect of the physical realm to gain enough investiture to affect the cognitive realm/spiritual realm to affect the physical (by changing various forces of attraction, repulsion, etc). That’s not even including Metallurgy which is its own thing.
I definitely recommend reading the Mistborn series where you’ll see his magic system from a different perspective and start to see parallels.
But at the end of the day there’s
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Mental will or intent by somebody with a link or “investiture” to a worlds magic system.
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The things to be changed/affected in one or more of the planes of existence by using the spiritual investiture
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The investiture source usually from consuming something from one of those planes such as metals, life force, cognitive.
For example I think the Nightwatcher tends to impose some kind of cognitive cost for her boon which affects spiritual bonds. So even in Roshar you have the impact of multiple shards and can see how they tend to warp how the magic works.