Welcome to Ireland Reaching Out and apologies for the delay in replying to your message.
Unfortunately, it may be difficult to find information without a more specific place of origin. Most Irish record sources- church records, land records, census records- are based on specific locations. Until you know a specific location within Ireland, preferably a parish or placename, it may be difficult to do anything more with these records.
Do you have any documentation pertaining to the family that mentions any place names at all? This can include wills, marriage/death records, census records, letters, diary entries etc. Have you tried searching Ancestry.com for any mention of your ancestor?s name in member family trees or messages? Ancestry is also hosting some 'webinars' on their site at present. The latest, if you are interested, focuses on how to research Irish records when you are not sure where, specifically your ancestor came from.
There are some places where you can search online, however these websites do not have complete collections and many do not cover the period after 1900:
www.familysearch.org has a huge database of genealogical records including some church records for Ireland.
www.rootsireland.ie have a large collection of Irish Church records, however you have to pay to use this site.
http://churchrecords.irishgenealogy.ie/churchrecords/ have begun a project to upload Irish church records to their site free of charge. However so far only Counties Dublin, Kerry, Carlow and parts of Cork have been covered.
Some other websites that may be helpful are:
The National Archives of Ireland: http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/ - you can search the 1901/1911 Census on the National Archives page too
The National Library of Ireland: http://www.nli.ie/en/family-history-introduction.aspx
Ask About Ireland: http://www.askaboutireland.ie/griffith-valuation/ where you can see the Griffith?s Valuation for free
The National Archives UK ? genealogy search:http://www.nationalarchives.gov.uk/records/looking-for-person/
The Public Records Office of Northern Ireland: http://www.proni.gov.uk/index/family_history.htm
Irish Times: http://www.irishtimes.com/ancestor/index.htm
Irish Genealogy Tool kit: http://www.irish-genealogy-toolkit.com/
Remember to post any new information that you find here. The more information you post, the more likely it is that one of our volunteers will be able to advise or assist you. Also include information concerning which sources you may have already used so others may further your search.
Best of luck with your search