It’s hard to believe, but Clyde Tombaugh really did make his own telescope essentially from scratch. In an effort to try to understand how this was actually done, I hunted down old reference guides that would make the process plain. These images are from 1001 Celestial Wonders, published in 1931. For a complete account of the step-by-step procedure, and for a description of the materials Clyde might have made use of, go here.
Somehow, when you grind two glass blanks against one another, one goes convex and the other goes concave. I honestly don’t entirely understand this myself, even after reading about it extensively. But it works.
In the novel, Clyde does a fair amount of this work, especially early on, as he’s making the telescope that will get him, eventually, to Flagstaff and Lowell Observatory.
Clyde’s grinding post must have looked very much like this. In the stained glass window rendering here, you can see all these elements.