My question following is: How do we know if/when someone is properly ordained?
Or who has the authority to ordain?
Ordination is a function of the Church.
It is always done with the laying on of hands by a group of pastors (in Lutheran Churches without bishops) or by a bishop (in the Lutheran Churches that either retained or restored bishops). I am sorry, my collection of service books does not contain an altar book, so I do not have access to an ordination service to give you a specific quote.
In the LCMS, the pastor of the congregation is often thought of as the bishop of his congregation.
The ELCA, as well as the Scandinavian Lutheran Churches which never lost bishops, require a bishop with an accepted line of apostolic succession (In the ELCA, this is due to the communion agreement with the Episcopal Church, which provides the bishops until all of the bishops of the ELCA are within the same succession).
The Lutheran Confessions prefer the ELCA model. Quoting again from the Kolb-Wengert translation, this time from the Apology of the Augsburg Confession, Article XIV: “Article fourteen, in which we say that no one should be allowed to administer the Word and the sacraments unless they are duly called, they accept with the proviso that we use canonical ordination. Concerning this subject, we have frequently testified in the assembly that it is our greatest desire to retain the order of the church and the various ranks in the church—even though they were established by human authority.”
Sorry for the delay, I was trying to find that quote.