Ireland was a part of the UK from 1801 to 1921. A revolution aimed at securing an independent Republic broke out in 1919. In 1920 the Government of Ireland Act partitioned Ireland into a six county Northern Ireland and 26 county Southern Ireland. Northern Ireland was politically controlled by pro British unionists while Republican rebels won the Southern Irish elections.

In 1921 the rebels negotiated the Anglo-Irish Treaty with the British government. This gave Southern Ireland (now called the Irish Free State) the same status as Canada or Australia. That is the King remained the head of state but the country had full control of domestic and foreign policy. Partition was to be re-examined by a commission.

The Irish Free State

The Treaty sparked a two year civil war between those who supported it and those who wanted a full Republic. The pro-treaty side won.

The new state behaved independently of Britain from the beginning. It set up embassies and joined the League of Nations.

In 1925 the Boundary Commission recommended only minor changes to the border with Northern Ireland. It's report was quietly shelved.

From 1932 the Irish Free State (IFS) worked to dismantle the Treaty. The provision for Irish parliamentarians to take an oath to the King was scrapped, as was the right to appeal legal cases to the British House of Lords. In 1936 all references to the monarchy were removed from the constitution.

ÉIRE 1937-49

In 1937 a new constitution was adopted replacing the King with an elected President. Although the country was not declared to be a republic, it effectively became one. The state was renamed Ireland or Éire.

In 1938 an agreement with Britain was negotiated which led to the closing of the last British naval bases in Éire. In world war II, Éire was neutral.

The Republic of Ireland

In 1949 the Republic of Ireland was declared and Ireland left the Commonwealth. Britain passed the Northern Ireland Act confirming that Northern Ireland would remain British.

Partition was the main point of contention between Ireland and Britain. The outbreak of the Troubles worsened relations. A better relationship was established by the 1980s leading to the Anglo-Irish Agreement of 1985 which gave the Irish a consultative role in Britain's running of Northern Ireland. The peace process of 1994-98 further improved relations.

Also important to developing Anglo-Irish relations was the two countrys' membership of the EEC.

I hope this is reasonably clear. Please ask any follow up questions you like.