How did Protestants first come to Ireland? The short answer to your question, is that the English government wanted the people in its Irish possession to be members of the Church of England, so the English government started sponsoring settlements of Englishmen in Ireland.
Two factors to consider: 1) England had conquered Ireland, but not the Irish heart: Irishmen were proving hard to rule; they remained very rebellious. Most of the Englishmen who had gone to Ireland, even those who had been sent there to rule Ireland, had become Irish in their sympathies. Making Irishmen more like Englishmen might make them easier to rule. 2) Henry the VIII had recently kicked the Roman Catholic church out of England and replaced it with the Church of England. The Church of England and the English government wished to also kick the Pope and his church out of the English possession of Ireland.
Both queens Mary and Elizabeth I had established small colonies of English Protestants in Ireland. These were called plantations. When James I became king of England in 1603, he believed that doing this on a larger scale would bring more success—more Englishmen was what was needed. James started a very large plantation project in Ulster, northern Ireland. The people he sent into his plantation were mostly from Scotland and Ireland. They were people who still retained some of their Celtic ways like the Irish, only not as much so, but they were Protestant like the English and they had accepted English rule.
In 1560, the Scottish Parliament had banned the Roman Catholic Mass; Scotland became Presbyterian. Presbyterian practices would be carried from Scotland into Ulster and from Ulster into British America.
From 1610 to about 1633, the Church of Ireland, a branch of the Anglican Church with the King of England as its head, recruited Scottish clergy to fill ministerial roles in its Ulster parishes.
During the reign of King Charles I of England, the Irish nobles rebelled and attacked the Presbyterians in northern Ireland. The Scottish Covenanting Party sent an army to put down the rebellion. Among its troops were ministers. A number of the army chaplains created the first presbytery in Ireland on June 10, 1642.
When Charles I tried to force the Church of England upon the Scottish people, a lot of them moved to Ulster where the Presbyterian church was still tolerated alongside of the Church of England.
When Oliver Cromwell became ruler of England, more Scottish Presbyterians moved to Ulster to escape Cromwell's oppressive economic policies.
Most of this answer comes from Barry Vanns book, Rediscovering the Souths Celtic Heritage (2004), p. 114-121.
The method, strictly speaking, was conquest, but not because of Protestantism. English adventurers first came to Ireland in AD 1169, under "Strongbow", the Earl of Pembroke. He was aiding the dispossesed lord of Leinster, which began a rather shameful episode of Anglo-Irish relations not ended to this day. Protestants did not come to Ireland until the 1530s, when King Henry VIII of England declared the Act of Supremacy in 1534, the declaration of English Protestant secession from the Church of Rome. From that point on English warfare against the Irish became by definition Protestant warfare against Irish Catholics.
By 1586 the Plantation System was in full swing, in which land was only owned by English and Scottish settlers, not the Irish. The Protestants could rent to Irish, but the Irish were no longer allowed to own land in the area of Ulster, in the north, and this spread to a large extent into the rest of the country. The most brutal phase of English warfare in Ireland occured under Oliver Cromwell, beginning in 1649.
On 11 July, 1689, forces under the deposed king of England (and Scotland and Ireland) James II and William of Orange, the new English monarch, met in the Battle of the Boyne. Oddly enough, though this is usually viewed in Ireland as a Protestant-Catholic struggle, since William's major political ally was the contemporary Pope. The victory by William ushered in an era of vague promises of fair treatment to the Irish, which were of course ignored by the victorious English leadership. These condition led to what is termed the Protestant Ascendancy, where in the 18th century Irish land ownership was reduced to 14% of land in Ireland. After 1704 Irish could not buy land, and all Irish held land had to be inherited by all sons, thus reducing Irish landholdings eventually to only small plots of land.
Essentially, Ireland was left a land ruled by Anglican lords, worked by Scots-Irish (ie, Scots who moved to Ireland) Calvinists, with the Irish Catholics reduced to poverty. This, of course, led to the conditions which resulted in the Potato Famine, the flight from Ireland of a vast percentage of its population, and eventually the rise of revolutionary movements. The revolution against England which began in the 18th century and has continued on to this day was, ironically, started by Wolfe Tone, a Protestant of English descent. Throughout the various Fenian uprisings and through the 1916 Rebellion and the Anglo-Irish War many of the leaders and soldiers fighting for Irish independence were Protestant. The only area of extreme Protestant-Catholic antipathy has been in Northern Ireland, an area containing part of Ulster (six counties) which since the Plantation days has been ruled ruthlessly by the small Anglican minority, who pit the working class Presbyterians and Catholics against one another.
It's important to remember that the real problem was never one of religion, but political oppression of the native population of a Celtic country by the invasion of a different ethnic group, the Anglo-Saxons. Although much of the conflict through the centuries has been couched in religious terminology, it has been economic oppression that has always been the main issue.