The process will vary slightly from diocese to diocese. I’m in Formation in the Archdiocese of Detroit, so I’ll give you my experiences.
In Spring and early Summer, the Archdiocese holds informational seminars for the deaconate. They will talk about the program, what’s expected and have several deacons and their wifes there to talk to.
I picked up my application at one of these last summer. The application process takes about a year in total.
The first part of the application is actually an application to the seminary here for courses. That involves submitting your transcripts from high school and college. You also register for your first classes. The program in Detroit results in a BA in “Deaconal Studies”
The coursework required is outlined here:
Link Here
At this point, you are paying for the classes yourself, though there are ‘scholarships’ available. As my wife and I do Marriage Encounter weekends and are active in marriage prep at our parish, I was eligable for a ‘parish teachers’ scholarship that covered 75% of the costs. So out of pocket for 4 credit hours each semester was about about $230 each semester plus books.
While taking classes your first year, you also fill out a lot of informational forms, get copies of your baptismal certificates, including records of your confirmation and marriage.
You also go through an FBI and State Police background check and both medical and psychological exams.
The Vocations board reviews this information, plus your transcripts for your first year at the seminary and makes a recommendation to the Bishop in late May. The Bishop gives an approval to the applicants and you are formally accepted into the process ( I got my letter last week

)
After that, you continue taking classes at the Seminary,( but the Archdiocese is paying for it now) and attend Formation instruction 1 Saturday each month. This is your ‘Aspirant’ year where you are in official discernment. Your wife is encouraged to attend classes with you and the Formation days as well. There is a yearly weekend retreat for all those in Formation as well as their wifes.
After the ‘Aspirant’ year, you officially become a Candidate. This phase will be about 2 years long and includes an Internship at a parish with a deacon.
After that is Ordination.
(Note that even though you have an official ‘discernment’ year, you can resign from the program at any point prior to Ordination)
Detroit Sue can probably add a bit more too, her husband is a Deacon who was recently Ordained in Detroit as well.
I hope this helps!!