I always wondered this as a jw but never got a straight answer and I asked GB members directly.
Pretty much it was
1) Prayer
2) Reading the scriptures
3) Discussion with other mature brothers (in this case GB members)
4) Prayer
5) Somehow it would come to them and it would be unanimous (definition meaning that those with the minority vote would give in to the majority--2/3 majority required to pass--per Ray Franz)
Here's the basis of the statements to me (just reporting not supporting).
*** w77 3/1 pp. 156-157 pars. 12-16 Congregation Elders—"Preside in a Fine Way"! ***We can learn much about the value of humility and the factors that serve to resolve disputes by considering what happened at a meeting of apostles and older men in the first century. The record is found in Acts chapter 15. It was at Antioch in Syria that Paul and Barnabas "had been entrusted to the undeserved kindness of God for the work they had fully performed." (Acts 14:26) But on returning there from that first missionary journey, they encountered a problem: "Certain men came down from Judea and began to teach the brothers: ‘Unless you get circumcised according to the custom of Moses, you cannot be saved.’ But when there had occurred no little dissension and disputing by Paul and Barnabas with them, they arranged for Paul and Barnabas and some others of them to go up to the apostles and older men in Jerusalem regarding this dispute." (Acts 15:1, 2) Here was a major doctrinal matter causing considerable disturbance to the brothers. It had to be resolved.
Appropriately, the problem was brought to the attention of the responsible elders at Jerusalem. The Bible record tells us what took place. Though there were differences of viewpoint initially, they finally reached "unanimous accord." (Acts 15:25) But in view of what Acts 15:7 says, was there not "much disputing" at the meeting? The Greek term for "disputing" is related to the verb meaning "to seek" (KingdomInterlinearTranslation); it thus indicates that to find the truth, or the best manner of doing something, diligent effort is required in searching out a matter—questioning, discussing things and thus arriving at a right conclusion. With this thought in mind we can read the account with interest, noting how developments were guided by holy spirit. After "much disputing," Peter related his experience in being used by Jehovah to open the way for Gentiles to hear the good news. He raised a question as to whether it was reasonable to impose burdens on such Gentile believers since it is God’s undeserved kindness through Jesus Christ that makes salvation possible. Next, note the respectful silence mentioned in verse twelve as Paul and Barnabas added their testimony. These traveling apostles ("sent forth ones" from the Antioch congregation) had received evidence of God’s blessing by "many signs and portents" as they preached among the nations. This supported Peter’s recommendation of what should be done.—Acts 15:7-12. Then James requested to be heard. He drew on the words of the prophets, such as at Amos 9:11, 12, which agreed with what Peter had related and confirmed what God’s spirit had accomplished through Paul and Barnabas. James thus had the support of the Scriptures and backing of God’s spirit for his decision. From that strong position he proposed that they write to those believers from the nations who were turning to God, telling them what God’s requirements really were for them. The apostles and older men had come to a unanimous accord. A controversial matter had been resolved in all humility.—Acts 15:13-29. If "unanimous accord" is not possible in a body of elders, one with a different view should not take exception to what has been decided by showing a spirit of animosity. He will want to continue to "work hard" with the whole body. The congregation will thus retain confidence in them, knowing that all are working in unity. Walking with "complete lowliness of mind" elders will be strengthening the bond of peace.—Eph. 4:2, 3.
