Before I start just to clarify Irish in this context relates to mainly Catholic Nationalists unless stated otherwise. The South, Irish Free state and 26 counties all relate to the Republic of Ireland while the North, 6 counties, Ulster relate to Northern Ireland.
Ireland was "split" in two in 1921. As part of the 1922 Treaty the 6 counties Antrim, Armagh, Tyrone, Fermanagh and Derry would remain with the UK and is called Northern Ireland while the other 26 counties became the Irish Free State. Northern Ireland was an autonomous part of the Free State and could vote to remove themselves from the Free State, which they did 2 days after The 1922 Treaty was signed. The split occurred due to both religious and political reasons with mainly Protestant Unionists campaigning to remain with the UK and the mainly Catholic Nationalist 26 counties campaigning for complete independence.
The origins of the split go back to the late 1500's early 1600's with the plantation of Ulster. In order to subdue the Irish, successive English Monarchs had tried to move English settlers ti Ireland with the hope the Irish would eventually be Anglicized. These had all failed except for the Ulster Plantation under King James 1. Plantations worked by first forcing the native Irish inhabitants off the land and then giving the land to English protestants or Scottish presbyterians who would build defensive houses and farm the land. Naturally this caused the native Irish to resent the 'planters' and sectarian violence has been a defining feature of the area since particularly during times of upheaval such as the English Civil war. the 1798 rebellion, the Irish war of Independence and of course the recent Troubles.
Fast forward to the start of the 1900's, Ireland was in the middle of a cultural revival with the setting up of the Gaelic athletic association and a renewed interest in the Irish language, history and culture. John Redmond's Irish Parliamentary Party, a moderate nationalist party, had been campaigning for Home Rule. If passed Ireland would remain part of the UK but would have their own parliament much like Scotland has today. In 1914 the Home Rule Act was approved by the House of Parliament but was delayed by the House of Lords and then put on hold until after the First World War, however this would not happen.
As Redmond was campaigning for Home Rule, Unionists, particularly Ulster, were campaigning against it feeling a Catholic majority government would persecute them and would damage economic ties with Britain which they relied on. A common slogan was "Home Rule is Rome Rule". The fear among Irish Protestant Unionists was so great that in 1912/13 they formed the Ulster Volunteers later the Ulster Volunteer Force (UVF), a well armed militia that would resist Home Rule. In response Redmond and fellow Nationalists like Eoin Mac'Neill set up the Irish Volunteers in 1913 to make sure Home Rule went ahead. When World War One began most members of the Volunteer forces joined the British Army. The Unionists joining to defend their country and show they were dedicated to Britain and the Nationalists joining to fight for the rights of small nations invaded (Belgium) and to ensure Home Rule would be enacted. Both Forces suffered huge losses in the Somme 1916.
Meanwhile in Ireland, a small band of Volunteers infiltrated by a radical Republican organisation the Irish Republican Brotherhood (IRB) staged a doomed Rebellion in mainly Dublin during Easter Week 1916 in a bid for Independence with the slogan "England's difficulty is Ireland's opportunity". The 1916 Eater Rising failed after 8 days with most of Dublin destroyed and hundreds killed and wounded. The Rebellion was widely seen as a stab in the back, verification Home Rule was a bad idea and an insult to the Volunteers fighting in France especially by the wide Irish public.
However opinion changed when thousands of innocent people were arrested and 90 people were sentenced to death. Most of the leaders were executed however the executions were stopped when the British Government realised public opinion had shifted.
The 1916 Rising was a major political turning point, radicalising the Irish public against the British Government eventually leading to the Irish War of Independence 1919-1922. While the War of Independence raged on throughout the country the British Government partitioned Ireland in 1921 creating the 6 counties of Northern Ireland.
In 1922 Irish and British Delegations met to find a resolution. The Peace Treaty the would force the Irish delegation to recognise the state of Northern Ireland as separate to the new Irish Free State. However there would be a border commission that would be set up to re-examine the borders of Northern Ireland where pockets of the North with Nationalist majority could become part of the South and vice versa. The hope of the British and Irish delegation was that after the border commission Northern Ireland would be too small to sustain itself and have to join the Irish Free State. This would not be the case and Northern Ireland is still in existence today.
Sorry I don't have references, This is all from memory except for a check on dates. If there is any part you'd like more info on let me know and I will happily locate a decent reference.