Most of those of the Catholic faith at one point knew how to address the various levels of church clergy properly, both in person and by letter. Formality and doctrine was a part of every Catholic child's religious training. Bishops and priests were clearly recognised by the faithful as a distinct class apart, occupying a special place in the religious society. These days, a priest might be seen often without clergy robes, dressed down to clothes anyone might wear. While not necessarily wrong, this does confuse the issue to some people about the level of formality necessary when writing to a priest.
To understand why the issue of proper etiquette even matters, first consider a bit of the church's history. The Catholic faith is built upon centuries of doctrine and custom that have seen a level of upheaval in the modern world, but it still struggles to hold close to the idea that a person should show respect to superiors while, at the same time, those occupying superior positions, such as priests, have a duty to treat those below them with dignity and consideration.
When writing to a Catholic priest, there are a few formal rules to follow to show him the proper respect his position suggests. A critical factor to consider is the matter of salutation and how to open the letter. The three basic options depend on the particular circumstances. For the purpose of demonstration, the priest in question is named William Walters.
If the letter is formal, the opening title should read "The Reverend Father Walters."
For a personal letter, it is permissible to shorten it to "Father Walters."
If you know him even better than that, you could write "Dear Father Walters."
There are no strict procedures for how to fill the body of the letter other than to stay respectful and on subject. In closing, it is fine to write "sincerely" and then sign your name. Also keep in mind that though it is fine to ask for the priest's blessing, it would be awkward to bless him. Blessings roll the other way within the customs of Catholic tradition.
Community and Orders
If the priest is a member of a particular religious order, it is appropriate to include the initials of the order after his name in the salutation, such as "The Reverend Father Walters, O.F.M. Remember, if he has taken the vows of poverty, chastity and obedience but not yet been administered the Sacrament of Holy Orders, the word "Brother" would replace "Father."