“The question being, how can you tell which authority is ordained by God?”
When you accept that you do not have the right to go in to any random church and demand to select its leaders, then recognizing legitimate leadership comes down to following the leadership of the local church where God directs you to be in fellowship.
This needs to be a church that proclaims the Word of God. A believer who sincerely seeks God’s will in this matter and is listening to God’s direction will find believers with whom he or she can fellowship.
The general qualifications of church leaders are specifically listed in several places in the Bible. It should be apparent that these are followed.