The clustering algorithms used in stylo are some of the most popular ones, the default is Ward's method, and other implemented options include:
"nj" - Neighbor joining, "single" - single link, "complete" - complete-link, "average" - average-link, "mcquitty" - McQuitty's, "median" and "centroid". Good descriptions of each of the methods can be easily found online, and you can change clustering algorithm used by calling stylo with proper parameters, e.g.: stylo(linkage = "nj")
And if you are looking for a general introduction to how clustering algorithms work, there are many nice introductions online, either more math-oriented or giving basic idea of the concept and methods, Stanford's is fairly good.
Best,
Joanna Byszuk