As discussed, sharpening is concerned more with subjective judgement than a measurable process.
Certainly there are obvious artifacts to look out for, such as the dreaded halos, but ultimately what and how much you sharpen is down to your personal taste. You may, for example, disagree with some of the results here and on the following pages, and that is as it should be. Your taste is the final arbiter.
Although Photoshop has Sharpen, Sharpen Edges, and Sharpen More filters, these are rough and ready, and allow no fine-tuning, so are best ignored. The usual professional sharpening tool is the Unsharp Mask. As a way of increasing sharpness, this sounds like an oxymoron, but the apparent illogicality is because the term is a holdover ...