How do you pick someone for a calling? Do you just ask the Lord and He somehow tells you who He wants? Or do you just pick someone that you like and ask God if He approves? How does that work?
Calling someone to serve the Lord uses the exact same process we are instructed to use to seek any revelation from God. I personally like the instructions the Lord gives Oliver Cowdery in D&C 9:7-9
7 Behold, you have not understood; you have supposed that I would give it unto you, when you took no thought save it was to ask me.
8 But, behold, I say unto you, that you must study it out in your mind; then you must ask me if it be right, and if it is right I will cause that your bosom shall burn within you; therefore, you shall feel that it is right.
9 But if it be not right you shall have no such feelings, but you shall have a stupor of thought that shall cause you to forget the thing which is wrong; therefore, you cannot write that which is sacred save it be given you from me.
From this instruction to Oliver we can see what the Lord expects. We should follow this pattern. The first step is to ask the Lord in prayer. The next step is to study it out. Or in other words, do some work. Use the talents God has given you to prayerfully work out what you think is the best answer. In the case of callings you should be studying people. Their situations, their talents, and their needs. Plus the needs of the calling and the people affected by this calling.
As one prayerfully studies the issues they should pay attention to both their heads and their hearts. As one does this, one opens themselves up to hearing the inspiration of the Lord. An answer might come to mind that you might not have otherwise thought of, or it might not, but as part of your studies and labor in this manner, you reach a choice that you think is best.
Ideally at this point you have the answer from the Lord. But we are all flawed humans and it is possible that we made a mistake or came to the wrong answer. Which is why we have one final step. We take our answer to the Lord. We tell him, “Lord this is what I am going to do.” Then we pay attention. We may get the “burning in our bosoms” or however it is we understand the Lord’s approval. Or we may get the disapproval that causes us to forget and feel incomplete. If we have the Lord’s approval, then we move forward and act as we planned. Otherwise we go back to studying it out.
This is the pattern that should be followed. Each leader will do so depending on his or her own understandings, needs and circumstances.
The leader also needs to understand that callings do not remove agency to the person called. Just because a leader knows who God wants and has called does not mean that the person will accept the calling. It can be very difficult for some leaders to work very hard to find just the “right” person, only to have that person say no. It might cause them to doubt that the Lord is indeed answering, or maybe cause them to think they did something wrong. But we must remember that the whole point of this life is to for us to choose to do the things the Lord commands, and the Lord will not take that choice away.