Maewyn Succat was born in Scotland some time around the year 373 A.D. At age 16, he was kidnapped and sold into slavery in Ireland. During his time as a slave, he started having religious visions. St. Patrick wrote in his "Confessions" about the capture:
"As a youth, nay, almost as a boy not able to speak, I was taken captive ... I was like a stone lying in the deep mire; and He that is mighty came and in His mercy lifted me up, and raised me aloft ... And therefore I ought to cry out aloud and so also render something to the Lord for His great benefits here and in eternity -- benefits which the mind of men is unable to appraise."
While tending sheep, he experienced a dream or vision in which God told him his ship had come in - which he interpreted to mean that it was time to run away.
He took the name Patrick, or Patricius, meaning "well-born" after becoming a priest. He was ordained as a deacon, then priest, then bishop before Pope Celestine sent him to Ireland to spread the gospel -- it is thought that his "driving out of the snakes" is a reference to his appropriating of the pagan culture, as serpents were pagan symbols.
Tradition has it that St. Patrick challenged demonic forces during a pagan feast, and that darkness fell over the area and confused the Irish guards of the king to start attacking each other.
While not the first to bring Christianity to Ireland, it was Patrick who encountered the Druids at Tara, converted the warrior chiefs, and baptized them in the Holy Wells which still bear his name.
Shamrocks are significant to Saint Patrick's Day because legend has it that Patrick used its three leaves to teach about the holy trinity; four-leaf clovers, being harder to find than the three-leaf variety, were seen as "special" and became symbols of good luck. There's no verification that St. Patrick actually used the three-leaf shamrock to teach the Trinity - however, the Trinity was central to his teaching.