Let's start with a word study:
Church = "The company of all Christians regarded as a spiritual body" (http://dictionary.reference.com/search?q=church)
Of = "Derived or coming from; originating at or from" or "Belonging or connected to" (http://dictionary.reference.com/search?q=of)
Christ = "The Messiah, as foretold by the prophets of the Hebrew Scriptures" or "Jesus" (http://dictionary.reference.com/search?q=Christ)
Thus, the "church of Christ" is "the company of all Christians regarded as a spiritual body, originating from or belonging to the Messiah, who is Jesus."
The church of Christ is not a denomination made by man, but it is the church that was promised by the Lord while He walked this earth (Matthew 16:18).
No denomination can make that claim, as all denominations were formed by man centuries after the Lord ascended into heaven.
Only the church that originated from Jesus Himself is acceptable.
Of course, it takes more than just the words "church of Christ" on the sign out front to identify the Lord's church.
What is practiced and taught by the congregation will reveal whether or not they are conforming to the Lord's will and seeking Him (Colossians 3:17; Hebrews 11:6).
Man does not have the authority to decide how one becomes a member of the Lord's church.
That authority rests solely with the Lord Himself.
In Acts 2:47, we are told, "And the Lord added to the church daily such as should be saved."
Peter didn't do it; Andrew didn't do it; John didn't do it; the Lord did it.
Those who repented and were baptized by the Lord's authority (Acts 2:38, 41) were those that the Lord added to His church (Acts 2:47).
It is the only way revealed in the Scriptures.