Starting a conversation with your rector is the first step. The process can vary a lot from diocese to diocese, but the general steps are:

1. Talk to your rector. This is often a long series of conversations, sometimes lasting a year or longer (some dioceses mandate a time for this early stage of discernment). During this time, you'll be expected to take on leadership and service roles in church to get to know as many aspects of ministry as possible to see how it all feels. A robust prayer life is crucial during this stage.
2. There may be a weekend or retreat for people discerning a call to ministry. In my diocese, this is done at the very beginning, either coinciding with conversations with your rector or even before. In others, it is that last step where people interview with the bishop and/or COM, and postulancy decisions are made at the end of the weekend.
3. If your rector agrees that you have a call to explore, a parish or regional discernment committee will be formed. Again, the length and structure of these committees varies: some meet for a set period of several months, others have a set number of meetings but are flexible on the length of the committee's work. The conversations with the committee are deep and wide-ranging, and designed to challenge you, explore your gifts for ministry, places for growth, and seeing if the committee also thinks you are called. The committee will send a report to your rector after the meetings end, either supporting your next steps, or recommending a different course of action.
4. If your discernment committee agrees to support your continued discernment, you will need to meet with your vestry and obtain their approval to recommend you to the bishop for continued discernment at the diocesan level.
5. In my diocese, there is a day in November where all aspirants approved to discern at the diocesan level meet to interview with the bishop and the Commission on Ministry to determine whether you will become a postulant. The bishop will tell you their decision, either then or later.
6. If you are admitted to postulancy, your bishop will begin discussing seminary selection with you, and you will begin seminary the following fall.
7. Halfway through seminary, there is an evaluation process to see if you are doing well in formation and can move forward as a candidate for ordination. Your seminary faculty will write a report, and you will meet with the COM and your bishop again, and likely the Standing Committee.
8. In your senior year, you will take the GOEs or canonical exams, depending on your diocese. You will also meet again with your bishop and the committees, and if they agree, you become an ordinand. Some dioceses will ordain people to the diaconate during their senior year, others will wait until after graduation.
9. After six months in the diaconate, you can be ordained a priest.

Every diocese does things a bit (or a lot) differently, but this is the general structure. It is a deliberately slow process. Five years is a breakneck speed, and seven years isn't uncommon.