Irish records are organised by place before they are organised by name, so a county is where a search actually becomes possible. Everything below is free, and every link goes straight to the Cork part of it.
Get a place before you chase a name. A surname on its own, even a rare one, is a needle in a national haystack; a surname and a county is a start; a surname and a parish or townland is the key that opens nearly every record below. If you only have a county so far, that is what this page is for.
The full method, step by step, is on the guide. This page is the Cork shortcut through it.
7 free sources, each filtered to the county. The 1901 and 1911 censuses are the place to begin: they are complete, free, searchable, and they are the only two full censuses of Ireland that survive.
This site places 60 surnames in Cork. If yours is among them, the page will tell you the Irish form, what it means and where the family came from, which is often the fastest way to turn a spelling in a register into a place on a map.
Ahern · Barrett · Barry · Buckley · Cagney · Canavan · Carew · Carey · Casey · Coffey · Coleman · Collins · Condon · Coughlan · Cronin · Crowley · Culloty · Daly · Deasy · Dennehy · Desmond · Díaz · Dinneen · Donegan · Donovan · Dowling · Downey · Duggan · Flynn · Foley · Forde · Galvin · Hayes · Healy · Hennessy · Hore · Hurley · Kelleher · Lombard · Looney · Lynch · McCarthy · Moynihan · Murphy · Noonan · O'Callaghan · O'Donoghue · O'Driscoll · O'Keeffe · O'Leary · O'Mahony · O'Sullivan · Regan · Riordan · Roche · Scanlon · Sheehan · Sweeney · Twomey · Woulfe
Not there? The full A–Z has 285, and the corrections form is how the last few got added.
Civil registration districts, parishes and Griffith's are all indexed by place, so knowing the town is worth more than knowing the decade. Cobh, Cork, Kinsale, Youghal have pages here, and the county page has its history, its rulers through every age and its castles.
The Public Record Office in Dublin burned in June 1922 and took centuries of material with it, including most of the 19th-century census returns. It is the reason Irish genealogy works the way it does, leaning on Griffith's Valuation and the parish registers to do the work a census would do anywhere else. The guide explains what survived, which is more than people expect.
These cover all 32 counties and are worth knowing whatever county you are working in.