One of the factors in visibility—at least, for “a clear day on a plain”—is the horizon. On an earth-sized and earth-shaped planet, using feet and miles, the horizon is the square root of the height of the eyes looking in feet; multiply by 1.346. That’s the horizon in miles. So on a perfectly clear day on perfectly “flat” land, a six foot tall person can see a little over three miles.
Usually, however, the question of how far someone can see is in reference to how far can they see something. For that, you add the horizon of the thing they’re looking toward to their own horizon.
Our hypothetical six-foot tall person could see another six-foot tall person start coming over the horizon six miles away. Of course, people are small, so it’s still going to be tough to see someone’s forehead six miles away. This is more useful for larger things, such as towers and mountains.
A 200 foot tower will start to come over the horizon from 19 miles away (plus the horizon of the person looking). A 10,000 foot mountain will start to come over the horizon 135 miles away (plus the horizon of the person looking).
And the math can be reversed as well. A 200 foot tower comes over the horizon at 19 miles away; at 16 miles away a 150 foot tower starts coming over the horizon. This means that at 16 miles, 50 feet of the 200 foot tower is now over the horizon. A 7,500 foot mountain starts coming over the horizon at 117 miles, so the 10,000 foot mountain has 2,500 feet showing at 117 miles.
And of course, spyglasses and other farseeing devices don’t change this, unless they can peer through the ground. That is, if something is below the horizon, a (non-magical, at least) spyglass can’t bring it above the horizon. The earth is in the way.
This is easier to use with a table, rather than doing square roots at the table. I don’t see how to put an HTML table here, but I have one in my game book either in the PDF or under Designing Adventures.