There are two main series of law reports for Northern Ireland: the Northern Ireland Law Reports (NI), which began in 1925; and the Northern Ireland Judgments Bulletin (NIJB), previously known as the Blue Books, which was first published in 1970. These are shelved at Cw UK NI 100.
Appeals from Northern Ireland to the UK Supreme Court may also be reported in the UK law reports series.
There are also some transcripts of 'unreported' cases available via online resources, but these consist of the judgment only and are generally only available from ~1999 onwards.
For cases before 1925 try the Irish Reports, Irish Times Reports, or UK law reports series.
NI: Northern Ireland Law Reports
Example:  NI 281
NIJB: Northern Ireland Judgments Bulletin
Example:  NIJB 314
NICA: Northern Ireland Court of Appeal (neutral citation)
Example:  NICA 273
NIQB: Northern Ireland, High Court, Queen's Bench division (neutral citation)
NIFam: Northern Ireland, High Court, Family division (neutral citation)
NICh: Northern Ireland, High Court, Chancery division (neutral citation)
NICC: Northern Ireland Crown Court (neutral citation)
NIMag: Northern Ireland magistrates courts (neutral citation)
NICty: Northern Ireland county courts (neutral citation)
Print collections of NI Law reports are on Level 2 at CW UK NI 100
For online access see below: