The following is from Harper's Bible Dictionary and Nelson's New Illustrated Bible Dictionary, s.v. "synagogue".
Origin. The origin of the synagogue as an institution is not certain. Though synagogues are not specifically mentioned in the Old Testament, they came into existence sometime after Judah was taken into Babylonian captivity in the 6th century B.C. Babylon was a likely place for them to have begun.
By New Testament times, synagogues had become numerous and were playing a larger role in community life. They were social centers for Jewish activities and schools for their children. They might have been used as local courts and for scourging. Jesus predicted that they would do such things in their synagogues against those that He would send. Matt. 10:17; 23:34.
As far as scriptural evidence goes, there is no mention of God instituting synagogues, just as Jesus did not institute church as we know of it today. Both the synagogue and church, for whatever good intentions they may serve, are still the institutions of men and the outgrowth of men's traditions.
Buildings. The Jews may have first "synagogued" in homes, but evidence shows that they erected buildings for themselves early on. The remains of one has been identified in Alexandria, Egypt, which is thought to date back to around 230 B.C. Jewish synagogues were well established throughout the Roman Empire and were in Jerusalem by the time of Jesus. The earliest type of architecture was the basilica. The basilica has a central nave (the main part) with semicircular apse (a projection of the building), two or four side aisles, a narthex (vestibule or entry area), and a clerestory (high walls with windows over the nave). The Torah was placed in an ark (cabinet) on a platform where there were also lamps and a lectern.
Many churches are still patterned after the basilica style of architecture. The only buildings God commissioned were the Tabernacle of Moses which was a movable tent with articles in it and Solomon's temple. Exod. 25:8-9 and 1 Chron. 28. Christians did not build their own places of worship until Emperor Constantine was converted around 325 A.D. and Christianized the entire Roman empire.
Seating. The younger people sat in the back while the best seats up front were reserved for the elders. Jesus condemned this prideful lust for prominence in Matthew 23:6. Referring to the scribes and Pharisees, He said that they loved the chief seats in the synagogues. Clergy still love the chief seats in their congregations. Those platform chairs are typically large, elaborate, and upholstered for royalty.
Officials. A synagogue could not be formed unless there were at least ten Jewish men in the community. Jesus said that where two or more are gathered in His name, there He would be in the midst of them. Matt. 18:20. The synagogues had a board of devoted and respected elders who regulated the policies of the synagogue. One or more men were elected by the elders to be the ruler(s) of the synagogue. The rulers took care of the building and planned the services. A minister was in charge of the sacred scrolls, attended the lamps, kept the building clean, did the prescribed scourging, and taught the children during the week. The ruler appointed a delegate of the congregation to read the Scripture lesson, to lead in prayer, and to preach or comment on the scripture. The Torah was written in ancient Hebrew so an interpreter was often needed. Two or three almoners (one who distributes charity) took up money or other necessities for the poor.
The fact that Jesus habitually went to the synagogue, read from the scroll, and taught is not an endorsement of the synagogue system. Luke 4:16-20 records that Jesus was even driven out of the synagogue. In Matthew 10:17 and 13:54, Jesus and Matthew referred to them as their synagogues.
Different traditions of Christian churches have variations of these officers. In the Presbyterian system, the board of elders rule along with the pastors. They are equivalent to the minister in the synagogue. Deacons or ushers are selected to receive and count the offerings. They are the equivalent to the almoners. The ruling officers may be called deacons as in the Baptist tradition or may be priests as in the Episcopal tradition.
Paul recognized that God gave some to be apostles, some prophets, some evangelists, some shepherds (who are the elder-overseers), and some teachers. The King James Version used the term "office" when it generally should have been translated service. Rom. 11:13; 12:4; 1 Tim. 3:1; 3:10; and 3:13. The idea of ministry being an office a position is foreign to New Testament thought. It is not a New Testament term or distinction. These are functions--acts of servanthood--in the body of Christ. No such "positions" exist in the Kingdom of God, only in the kingdoms of men.
Order of worship. Before the service, the minister would place the Torah on the lectern and scroll it to the reading for the day. The service began with the Shema--the passage in Deuteronomy 6:4-9. The speaker for the day led in prayer--facing Jerusalem with hands extended--after which the people said, "Amen." He stood up to read the lesson for the day and sat down to sermonize upon it. Luke 4:20. Afterwards, if a priest were present, he would pronounce the benediction to which the people said, "Amen." If no priest were present, someone offered a closing prayer. The scriptures are still read and sermons are still preached in the churches today much as they were in the synagogues, following prescribed lectionaries for the week.
This format is in stark contradiction to the spirit-led, believer's meeting which the New Testament followers had, going from house to house. The Corinthians' meeting are pictured in 1 Corinthians 14:26: "How is it then, brothers? When you come together, everyone of you has a psalm, has a doctrine, has a tongue, has a revelation, has an interpretation." New Testament assemblies were characterized by the existence of the equipping gift ministries of apostles, prophets, evangelists, pastors (elders) and teachers; by the plurality of elders; by the operation of all of the gifts of the Holy Spirit; and by mutual recognition of one another's contribution to the body of Christ. Jesus said the Father was seeking those who would worship Him in Spirit and in truth (John 4:23-24), not according to a bulletin or dead ritual. I am convinced beyond doubt that if Jesus were to walk into most of the churches today, He would be treated much the same as He was in the synagogues in His day. The difference between what He called us to and what we have in church today is striking.