The requirements for the permanent diaconate seem to vary slightly from diocese to diocese. But it usually involves having attained a certain age (35 years old?), and if you are married, having been married for a certain period of time (8-10 years ?), demonstrate you can hold a steady job, be of sound moral character, be a man of prayer, etc. When a friend of mine applied to become a permanent deacon, the application process did not seem terribly different from when I applied to religious life. Which also wasn’t terribly different from applying to the priesthood (essay, medical exams, psychological exams, many letters of recommendation, etc). You can become a deacon if you’re married, but a deacon cannot get married (neither for the first time nor remarry if a spouse dies) after ordination to the diaconate.
Deacons are ordained clergy, along with priests and bishops. Deacons cannot preside at mass or hear confessions, but they can preach homilies at mass, assist the priest at mass, give blessings, baptize, witness marriages, conduct funerals, and a wide variety of pastoral ministry to the poor, sick, and grieving, or anyone else. They work for the bishop, who could assign them to any manner of ministry. When they are assigned to a parish, the pastor usually oversees them. Deacons also undergo quite a bit of training. In some dioceses that involves an academic degree, in others it involved several years of diocesan-run classes on theology, ministry as well as pastoral and spiritual formation.
This website outlines diaconate formation for the Archdiocese of Los Angeles, and is one of the more detailed descriptions I found online. It should give you a decent idea of their formation and what kind of ministries they prepare for.
http://www.la-archdiocese.org/org/odf/Pages/formation.aspx . Your diocese may vary slightly .