How do circulating androgens contribute to higher rates of hirsuteness in some women?
This review may be of interest:

Sharma D, Shanker V, Tegta G, Gupta M, Verma GK. Clinico-investigative profile of patients of hirsutism in a tertiary level institution. Int J Trichol [serial online] 2012 [cited 2013 Feb 9];4:69-74. Available from: http://www.ijtrichology.com/text.asp?2012/4/2/69/96904

As for the genetic causes of hirsutism, researchers thought the number of CAG repeats in the androgen receptor gene might play a role, but there was no evidence to that effect, as of 2000.  I couldn't find any newer papers, but here you go: http://jcem.endojournals.org/content/85/4/1735.
This paper was cited by the previous review, but Sharma et al didn't read more than the title, because they cited Calvo et al as evidence for the role of CAG repeats in hirsutism.

tl;dr: read Sharma et al, and look up the references.