How do individuals in polygamous relationships live?
Polygamists, who mostly reside in the Southwest United States, tend to live in close-knit communities, with families often housed in connecting structures or in separate houses that are right next to each other. Many inhabit and work on farms, or are employed in skilled professions like carpentry. Many are employed in the construction industry.
Polygamy was banned by the Church of Jesus Christ of Latter Day Saints in 1890, and modern-day polygamists are members of break-away factions of the church. A study by National Geographic estimated the number residing in the United States as between 30,000 and 50,000.
In general, polygamist marriages involve the husband moving among the multiple households he supports with regard to marital relations. Beyond that, the individual "families" attached to a single husband function as a community, with each member contributing in whatever way is deemed necessary.
While this answer assumes the question is focused on polygamy in the United States associated with off-shoots of the Mormon Church, a link below discusses the practice within the religion of Islam, as polygamy is practiced in some Islamic countries.