“Jethro, his father-in-law, the priest of Midian.” “Jethro” is the priestly name of Reuel, the father-in-law of Moses (see commentary on Judg. 4:11).
“and he led the flock to the far side of the wilderness.” The biblical culture was oriented to the east, so the “far side” of the wilderness is the far west side. In this context, it is not so much where any “wilderness” (desert) area ended, but where the territory of Midian ended.
It was not uncommon for shepherds to take their flock many miles from their home base. For example, Jacob’s sons traveled over 60 miles from home with their sheep (Gen. 37:17), and it is possible that Moses went at least that far. In 1855 Horatio B. Hackett wrote about the travel of shepherds that he encountered and heard about: “Another peculiarity of the desert is that, though the soil is sandy, it rarely consists, for successive days together, of mere sand; it is interspersed, at frequent intervals, with clumps of coarse grass and low shrubs, affording very good pasturage, not only for camels, the proper tenants of the desert, but for sheep and goats. The people of the villages on the borders of the desert are accustomed to lead forth their flocks to the pastures found there. … The shepherds not only frequent the parts of the desert near their places of abode, but go often to a considerable distance from them; they remain absent for weeks and months, only changing their station from time to time, as their wants in respect to water and herbage may require.a”