How is a Theravada Buddhist monastery established?
Initially, it is the invitation of the laity to the Sangha, who then satisfy themselves that the support is adequate for their needs.  A lay community invites a Bhikkhu that they find particularly inspiring.  He finds a quorum of Bhikkhus to accompany him so as to maintain the Vinaya discipline. Lay communities often set up some kind of a committee so as to oversee and organise a physical accommodation, suitable for practice and religious observations: this varies considerably from one monastery to another.