That's an impossible question to answer really, because it's too broad and unspecific.
You need to start with yourself and the family members that you know about and then work backwards one step and one person at a time...document as much of it as you can, and beware of the information in many of the trees on here.
Some of them are very well researched and documented, and contain accurate and proven facts, but many of them are complete tripe.
A lot of them are the result of someone importing stuff that they found on somebody else's tree and they just accept it as being correct and then that gets grabbed by somebody else, and so on.
It can soon get hard to keep track of all the people and kinships that you may find, so get some index cards and write the details of each person, and, seriously, get a roll of white lining wallpaper, and draw a tree on it and add each person and their main details, such as dates, that's visually much easier and intuitive to follow and keep track of the relationships of each person.
Some types of information and records are available for free, most of that has often to be paid for though.
Find out what your family knows.
Find what you can about the people that you know about, and then when you get stuck, ask a specific question on this site.
Local libraries usually have a lot of genealogy for beginners type books and some of them have internet subscription to genealogy sites which the library members can use.
You'll gradually find out about what records are available and from where as you go.
You'll find a bunch of vids about Irish genealogy on youtube.
https://www.youtube.com/watch?v=kNAQYS0j1UkThe LDS = Latter Day Saints = the Mormons, and they have been collecting all sorts of genealogy records for many years, a lot of ancestry's records were obtained from the LDS.
The site below is a free site provided by the LDS and it has a huge amount of information and it also has a lot of free records which are available online.
It also has free local family history centers all over the world in which there are staff who will help you and they can also order in records for you if they're not available onsite.
http://tinyurl.com/o6gy4ojhttps://familysearch.org/Their nearest site to you is in Limerick.
https://familysearch.org/locations/centerlocator?cid=hp2-104...Their records search engine is a bit clunky and fiddly to get the hang of, but it's a very powerful search engine.
https://familysearch.org/searchThey also have a lot of very good tutorials.
https://familysearch.org/learn/wiki/en/Family_History_for_Be...https://familysearch.org/learningcenter/home.htmlhttps://familysearch.org/learningcenter/results.html?fq=plac...https://familysearch.org/learningcenter/results.html?fq=subj...https://familysearch.org/learn/wiki/en/Ireland_Civil_Registr...http://www.irish-genealogy-toolkit.com/Ireland-civil-registr...http://genealogyresearch.org.uk/irl_registrationdistricts187...https://familysearch.org/learn/wiki/en/Ireland,_Civil_Regist...)
http://www.irish-genealogy-toolkit.com/Irish-civil-registrat...http://genealogyresearch.org.uk/irl_registrationdistricts187...You can get Irish birth, marriage, and death certificates for what is now the Republic of Ireland from the General Register Office of Ireland.
https://www.welfare.ie/en/Pages/General-Register-Office.aspxThe complete 1901 and 1911 Irish censuses have survived, and also some bits of the earlier censuses, and can be searched online for free, and that search engine is one of the best on the internet.
http://www.census.nationalarchives.ie/https://familysearch.org/learn/wiki/en/Ireland_Censushttp://www.irish-genealogy-toolkit.com/ireland-census-substi...Griffiths 19th century survey of Ireland is a very useful resource.
http://www.irish-genealogy-toolkit.com/Griffiths-Valuation.h...http://www.askaboutireland.ie/griffith-valuation/index.xmlhttp://www.irishancestors.ie/?page_id=5392https://en.wikipedia.org/wiki/List_of_towns_and_villages_in_...http://www.findagrave.com/www.cyndislist.comhttp://www.cyndislist.com/uk/You can search for and view and download, for free, WW1 military wills for soldiers who served in Irish regiments, ( the English charge for that for mainland soldiers ! ).
http://soldierswills.nationalarchives.ie/search/sw/home.jsphttp://www.cwgc.org/find-war-dead.aspxhttp://www.stpatrickscathedral.ie/Irelands-memorial-records....http://www.tcd.ie/Library/about/exhibitions/drawn-to-the-pag...http://www.irishtimes.com/news/social-affairs/records-of-49-...http://imr.inflandersfields.be/http://www.genguide.co.uk/source/mustermilitia-rolls-amp-mil...http://www.irishmariners.ie/http://www.benjidog.co.uk/Tower%20Hill/WW1%20Memorial.htmlhttp://www.benjidog.co.uk/Tower%20Hill/WW1%20Memorial.html#M...http://www.nationalarchives.gov.uk/records/looking-for-perso...http://www.nationalarchives.gov.uk/records/https://www.gov.uk/requests-for-personal-data-and-service-re...https://en.wikipedia.org/wiki/Registration_districthttp://www.genuki.org.uk/contents/http://www.ukbmd.org.uk/genuki/reg/http://www.freebmd.org.uk/DistrictInfo.htmlhttp://www.freebmd.org.uk/BTW Do you ever tell any of your American visitors that if they have or had a parent or a grandparent who was born anywhere on the whole island of Ireland, that they have Irish Republic nationality by right of descent. ?
Americans usually freak when they are told that. :):)
http://tinyurl.com/nuyvm3gErin go bragh.