How did the Apostles organize the church?

Early Christian churches had their own leaders because each local church was autonomous there was no such thing as a head bishop in Rome, this was something invented later by men.

In the New Testament you can see that the leaders of the local church were the elders:

Act 14:23 So when they had appointed elders in every church, and prayed with fasting, they commended them to the Lord in whom they had believed.

1Timothy 5:17 Let the elders who rule well be counted worthy of double honor, especially those who labor in the Word and doctrine.

Today, "bishop" means a church official who exercises authority over many local congregations. But invariably in the New Testament there were several bishops in one church - Acts 20:17; Philemon 1:1; James 5:14

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The same Word translated bishop in 1 Timothy 3:1 is translated "overseer" in Acts 20:28. A bishop, or overseer, is the same as an elder. The same men who are called elders in Acts 20:17 are called overseers in Acts 20:28 ( also Titus 1:5 and Titus 1:7).

Elders are the same as presbyters, for although the latter Word is not found in the NT, the English Word "elder" translates the Greek Word presbuteros. Thus, the Words "bishop," "overseer," "elder," and "presbyter" all refer to the same person.