There are two conferences addressed in scripture and history. They are Elders Conferences and General Conferences.
The Elders Conference
Elders conferences are held in stakes and districts and include all Melchisedec priesthood members representing the various congregations in the stake or district. Elders conferences are directed by the Doctrine and Covenants.
“The several elders composing this church of Christ are to meet in conference once in three months, or from time to time, as said conferences shall direct or appoint; and said conferences are to do whatever church business is necessary to be done at the time.” D&C 17:13
Please keep in mind when our scriptures refer to Elders, it usually refers to all those who hold the Melchisedec Priesthood. So the conferences that are called for in this revelation are for the Melchisedec Priesthood.
In the organized stake areas, quarterly conferences are relatively easy to conduct and are conducted by the stake president who will usually have a general church authority present for council and advise.
In unorganized areas it is the responsibility of the missionary in charge of the district or area of missionary endeavor, that is responsible for calling and presiding over quarterly conferences.
The General Conference
What is called a General Conference, (meaning the gathering of the body of the church for legislative purposes), was not instituted until after the reorganization, replacing, for the most part the general assembly setting. General Conferences outside of the General Assembly setting, were not recorded or prescribed in the time of Joseph Smith, Jr. It appears that a total gathering (as much as possible) for church participation in legislative matters, was within the general assembly setting. This was the case of the assembly that was called for when the Doctrine and Covenants was approved in 1835. It appears that most legislation was approved by the body in the various stake and unorganized areas during quarterly conferences.