Not trying to be flippant with this response, but by far the best way ... experience. There are so many variables (coin type, composition, age, etc.) providing examples is impractical. Is there a certain series you are interested in? If so, we could provide examples of natural and artificial toning on each and talk about the differences.
Here's an excerpt from a PCGS article on toning ... "The most obvious difference between natural and questionable toning is the way in which the toning "lies" upon the surface of a coin. When an original coin tones over time, the toning appears to be attached to the surface from the "bottom up." There is an appearance of depth to the toning and the colors are rich and natural looking. When a coin is toned quickly by the introduction of chemicals and/or heat to the coin's surfaces, the toning floats on the surface and the color lacks depth. The toning appears shallow and not "attached" to the surface, as with original color. The colors associated with this type of toning tend to be unnatural-looking, often called "crayon" colors because they look as though they were "colored" on the coin's surface-weak pastel colors "painted" by a first-grader."
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