How do statements become official positions of the Church?

They are sent in as petitions to General Conference every four years by general agencies, annual conferences, local churches, individual members, and groups. Once submitted as petitions, most of them are worked on by delegates in a legislative committee. The legislative committees accept, reject, or amend the petitions, then report their recommendations to the General Conference plenary; all delegates then vote on their recommendations. 

If you would like to submit a petition to General Conference, proposing a different statement regarding a particular subject, see information about the process in paragraph 507, "Petitions to General Conference," in the 2004 Book of Discipline.