Depends on the diocese pretty much. But likely the path will include, in the early part of your discernment process, a visit to both a licensed clinical phsycologist, who will inteview you and probably administer some well-established psychometric exam such as the MMPI, and to a psychiatrist (a physician).
Some people who articulate or personally feel a calling to ordained ministry simply may have problems that are hidden somewhat below the surface. It would take a trained, skilled professional to see it in many cases. Just a brief look at all the situations of scandal provides a very visible example that at least some misery could have been prevented by adequate screening. Is it perfect? No. No screening is. But is simply an exercise in due diligence. Just because a vocation to an ordained ministry is a holy calling does not mean that thoroughly unholy people or thoroughly unhealthy people won’t submit themselves to bishops for ordination. Due to the trust we want to be able to invest in our clergy, it only makes sense that if we put our trust in one who is not psychologically fit or able to undertake the stresses of ordained ministry, then we are asking for bad trouble.
Ask a victim of ANY kind of clerical abuse - physical, sexual, spiritual, psychological, or any other kind of abuse - if THEY would have liked the Church to afford them the chance to have been spared their grief by requiring psychological screening of the clergy.
The examinations are not “difficult” nor are they scarey. There is nothing to fear.
I have known of cases in which the requirement for psychological examination benefited both the Church AND the aspirant for Holy Orders who was initially held up after the psych exam. Some of these folks had things in their lives that had them psychologically unprepared to take on the tremendous responsiblities of being clergy, especially being parish priests. The exam showed these problematic situations, allowed the diocese to put the process on hold, the aspirants worked through the situations with professional help, and grew into candidates for Holy Orders who were ready to be wonderful clergy. These are the cases you don’t hear about - but they happen. These people didn’t just have their vocations thrown in the crapper. They were helped to address the needed issues, and then progressed on when they were ready.
The Church HAS to have processes in place as part of the discernment process. For ordination to take place, not only does the individual have to hear the “call”, but the Church has to also hear the call for that person to be an ordained minister. Ordination, among other things, is the Church’s ratification at the communal level, of what the individual initially heard as a private or personal call. But just as the Bible tells us to “test a spirit” to see if what it is telling us is true, so it is with those who offer themselves for ordination. Just because a person offers himself for ordination, it is not an automatic assumption that they should be ordained.
Hope that helps!