When Jesus promised He would build His church, He was speaking of the body of the saved (cf. Matt. 16:18). He did not specify any particular location; rather, He had the universal church in mind. On the day of Pentecost, the Lord added 3,000 souls to the church (cf. Acts 2:41,47). They were members of Christ's universal church. In practical terms they also were members of the newly formed Jerusalem congregation. Later, more congregations were established through the preaching of the word in other places. Soon a congregation of the Lord's people existed in Antioch, Ephesus, and Corinth to name but a few.
We live in a very mobile society today. People move around a lot. However, it was not much different in the first century. The Bible reveals that Aquila and Priscilla left Rome and moved to Corinth (cf. Acts 18:1,2). Today, when a Christian moves what should he do regarding his membership in a local congregation?
Sadly, some members of the church do nothing after they move. They do not seek out a faithful church with which to worship. Sunday becomes a day for family activities or to catch up on household chores. However, Monday morning finds them at work or in school. Such action reveals misplaced priorities (cf. Matt. 6:33). It is not possible to be faithful to the Lord while forsaking the assembly of the saints (cf. Heb. 10:24,25).
Thankfully, most Christians do seek out a church when they move. Some time and effort should be expended to check out the church or churches which one might be interested in attending. Sadly, it is not always easy to find a congregation of the Lord's people that is sound in the faith. Does the preacher deliver good sermons that are full of God's word? If not, it's time to look elsewhere. If the pulpit is sound, is the congregation active in the work of the Lord? If not, it may be time to consider other options if they exist. Do the brethren appear committed to doctrinal and moral purity? Though a preacher may be sound in the faith, sometimes a majority of the membership may be going a different direction (cf. Rev. 3:1-5). It's not surprising then that Christians take some time visiting area congregations to find a good one.
What makes a congregation good? That depends upon what a person is looking for. Congregations vary in size, average age, racial composition, location (rural, suburban, and inner city), etc. Some churches have nice buildings and lots of programs. However, the selection criteria of utmost importance ought to be whether the church is sound in the faith (cf. Titus 1:13).
Some people are "floaters." They never commit to one congregation but are always looking for the perfect church. They may skip Sundays and alternate between two or three congregations. With no dedication to a particular congregation, how likely are they to be faithful to the Lord? God says we can judge a person by his actions (Matt. 7:18-20; cf. John 7:24).
Once a Christian finds a good congregation he ought to attend there exclusively. Does regular attendance automatically make a Christian a member of that congregation? Not necessarily. Would he submit to rule of the elders? If he is not willing to make a commitment to a local congregation, can he be counted on for the work of the church? Might he become a floater?
Faithful Christians naturally desire to fellowship others of like precious faith (cf. II Pet. 1:1). Though the Bible does not command placing membership at a new church, we do have the example of Saul (later known as Paul) wanting to be associated with the Jerusalem congregation. Therefore, "when Saul had come to Jerusalem, he tried to join the disciples" (Acts 9:26). Thus, it is certainly a wise practice for a Christian who relocates to make his desire to be identified with a local congregation known to the leadership.