TL;DR: Natures raise one stat by 10%, and lower one stat by 10%, going off of what the stat would be without the effect of the Nature in play.
Natures were introduced in Generation 3 ( Ruby & Sapphire ). In Generations 3 & 4, Natures were determined through a Pokemon's "personality value", which controlled over factors such as shininess and gender. I could not tell you how exactly this works, but feel free to read the hyperlinked source for more information. However, after this, it was determined by a separate variable. What Nature a Pokemon has is completely randomized, not being dependent on IVs or any other characteristics of a Pokemon.
A Pokemon's Nature is assigned when you encounter it, or when it is an egg during breeding ( though the exact time while it is an egg depends on the game ). A Nature cannot be changed, though the mints introduced in Generation 8 change which stats a Nature impacts.
There are five Natures that are technically "neutral" — Hardy, Docile, Serious, Bashful, and Quirky. However, these are just a result of the Nature raising and decreasing the same stat by 10%.
Natures build off of both IVs and EVs. Let's use Arceus as an example, since all of its stats are 120 base. And let's say this Arceus has an Adamant Nature: +ATK, -SPATK. Calculations for this will be done here.
At Level 100, with a neutral Nature, 0 IVs, and 0 EVs, Arceus has a value of 245 for all of it's stats ( besides HP, which is irrelevant to the discussion of Natures ), meaning the stat changes from having an Adamant Nature should increase its Attack by 24.5, and lower its Special Attack by 24.5. Pokemon "rounds" all stats down, so it should be a change of 24 when raising, and 25 when lowering. Therefore, we can see that Arceus' ATK raises to 269, and its SPATK lowers to 220.
If we add 31 IVs to Arceus' stats, they raise to 276 ( 1 point per IV ). Since Natures build off of IVs, the stats would be raised / lowered by 27.6 starting at the value of 276, resulting in 303 ATK and 248 SPATK.
With 31 IVs and 252 EVs, the stat values would start at 339 — again, a change of 33 / 34 can be observed, with the new values becoming 372 and 305.
To answer your question as to whether it is multiplied or added — both, I guess. You could either say .1 x stat value + stat value, or 110% of stat value.
Feel free to ask any other questions you may have, I hope this clears up most of your concerns though.
