How is linguistic evidence used in Guns, Germs, and Steel to draw conclusions about the spread of peoples in Africa?
The answer to this can be found in Chapter 19. There, in Figure 19.2 and beginning on p. 383 in the paperback edition of the book, Diamond tells us that linguistic evidence shows that Bantu peoples spread across Africa, displacing speakers of other language families.
In Africa today, the speakers of Khoisan languages are scattered across the continent. The Pygmies, though ethnically different, do not have their own language family. Meanwhile, Bantu languages are spoken across essentially all of sub-Saharan Africa. From this, Diamond infers that the Bantus spread across the region. As they did so, they engulfed and displaced speakers of Khoisan in most places, leaving them in isolated "islands." The Pygmies simply adopted the languages of the Bantu who swept across their lands.
In this way, the distribution of languages in sub-Saharan Africa shows us that the Bantu spread across the region, engulfing other ethnic groups.