Jesus Christ founded, established, and developed the early Church systematically, as its size or complexity demanded. While alive, Jesus directed this growth personally since physical ministration was possible. After His resurrection, He continued to direct the Church expansion by revelation through the Holy Ghost as manifested in the lives and ministry of His ordained Apostles.
During the Savior’s lifetime, twelve apostles were called to minister upon those who didn’t have that good news. This number was set at twelve, after the suicide of Judas Iscariot, another witness of the Lord’s resurrection was ordained to replace Judas Mathias. It wasn’t the only leadership position Jesus established while alive or during their ministry. Christ also called 70 men (or 72, depending on which Greek manuscript you’re reading) to spread the good news of that gospel.
Following Christ’s resurrection, He continued to lead that Church personally for forty days, then through a Holy Spirit after ascension to heaven. Disciples had been promised before death that they would be given that Holy Ghost, which occurred at a feast of Pentecost, fifty days after death. With that Holy Ghost as a guide or messenger, apostles with other disciples could spread those teachings. They also taught news of atonement, resurrection, then continued presence with great power. Disciples performed miracles, taught, baptized, bestowed that gift of the Holy Ghost, and expanded that Church’s organization.
At first, Christianity was considered a sect of Judaism, and the Jewish disciples like Peter continued to observe its requirements in addition to the requirements Jesus had emphasized. But that sect faced a lot of persecution from Jewish authorities. As congregants began to include more Gentiles, many of the requirements mandated by Moses’ law were dropped for Gentile converts. This was done in an orderly way through leadership councils and by revelation from the Lord. Most of this development is outlined in the book of Acts in the New Testament.
The record of that early Church’s establishment is not complete because not everything was recorded. All that is known is what is contained in the New Testament. After the book of Acts, written by Luke, the New Testament was mostly written by Paul, letters penned to congregations they had established. Peter wrote many letters, probably dictated to John Mark. James seems to have authored one letter. Another one (the book of Jude) is considered to be the work of another of Jesus’s half-brothers. Three short letters and the book of Revelation were written by John, one of the original Apostles Jesus called during His lifetime.
Generally, it was established by Christ, who was sent from heaven to show the direction to people. Those who believed were baptized were then included in the Church list.