There are a number of steps to go though before a man may be ordained a priest.
Here's an overview:

Contact: Get in touch with the vocations office! They are a valuable source of information and work with men on a case-by-case basis to guide each individual through the discernment and application processs.

Candidate: Apply to Becket Hall and begin a formal period of discernment with other men considering priesthood. The required period of candidacy, or pre-theology, is 2 years. One of those is spent at Becket Hall.

Seminarian: The candidate, sponsored by the Diocese, enters seminary to begin his priestly formation and theological studies. At this point he is called a seminarian. There are generally
four years of seminary study, plus one year working in a parish of the diocese.

Transitional Diaconate: About a year before ordination to the priesthood, the seminarian is ordained to the Transitional Diaconate (so named because the seminarian is in transition to the priesthood, and to differentiate from the Permanent Diaconate). The transitional deacon makes promises of celibacy and obedience to the Bishop.

Priesthood: After much work, and a lot of prayers, the man is recommended for ordination to priesthood.

What should you do if you feel God may be calling you to priesthood?

"If some of you hear the call to follow Christ more closely, to dedicate your entire heart to Him, like the apostles John and Paul, be generous, do not be afraid, because you have nothing to fear when the prize that you await is God himself, for Whom, sometimes without ever knowing it, all young people are searching."
-Pope John Paul II (Asuncion, Paraguay; May 18, 1988)

• Get in touch with the Vocations Office.
• Talk to your parish priest, campus or youth minister, or others whom you trust.
• Pray often – ask God to reveal the plan for you. If you don't already pray the
  Liturgy of the Hours you may want to begin doing so.
• Get involved in your parish as an altar server, lector, Eucharistic Minister, greeter,
  singer, musician, etc.
• Join a discernment group (contact the Office of Vocation Awareness for details).

Are you in college?

• If you are at least 20 years of age and have completed 2 years of college, you may
  want to consider applying to the Becket Hall residential discernment program.
• Keep in mind the education requirements for entering major seminary:
  • a bachelor’s degree from an accredited institution
  • minimum 30 hours of approved philosophy courses
  • minimum 12 hours of approved religious studies
    (you can work on some of these requirements while living at Becket Hall)
    
  And, of course, full initiation in the Catholic Church is required. That is to say, you
  must have received the sacraments of Baptism, Eucharist, and Confirmation.