It was apparently one person doing the speaking for at least until the churches were well established.
All Scripture is quoted from the King James translation, unless otherwise noted.
Matthew 28:18 through 20 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth. 19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: 20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.
This would have necessitated that those do all of the talking since they would be the ones with the knowledge.
Paul was the founder of many Churches in the Gentile world, and from the following Scriptures we see that he did the talking.
Acts 20:7 And upon the first day of the week, when the disciples came together to break bread, Paul preached unto them, ready to depart on the morrow; and continued his speech until midnight.
The church at Jerusalem on the other hand was born out of the synagogues, and may have followed those old traditions:
Luke 4:16 through 19 And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read. 17 And there was delivered unto him the book of the prophet Esaias. And when he had opened the book, he found the place where it was written, 18 The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised, 19 To preach the acceptable year of the Lord.
It appears that it was common for others in the synagogue to read scripture and then comment on them.
So the answer to your question may be both, judging from what we can derive from Scriptures.