In the earlier years of migration ships sailed from some quite small ports around Ireland but by the mid to late 1800s larger steamships meant fewer ports were in use. There were regular weekly sailings from Londonderry to New York, Philadelphia, Quebec and St John NB (Canada used to be cheaper to get to so, if money was tight, US bound migrants might use that route and then cross the land border into the US). See example shipping advert attached:
http://donegalgenealogy.com/passengers.htmThere were also sailings from Belfast, Dublin and Queenstown (today’s Cobh) in Co. Cork. However, by far the biggest port of departure for the US & Canada was Liverpool which was a sort of clearing house for migrants from all over Europe. There were often several departures every day from Liverpool to New York, Boston etc. Competition for the business was fierce and many ships agents threw in the cost of the short passage from Ireland to Liverpool free, as well as a couple of nights accommodation in Liverpool. The reputation of the Liverpool lodgings was not good. Migrants often didn’t get very good treatment there. See this link for general background but also details of possible Irish sources eg the Irish Emigration Database in Omagh, Co Tyrone:
https://www.liverpoolmuseums.org.uk/archivesheet13Use this website to see where in Ireland a surname was common in the mid 1800s:
https://www.johngrenham.com/surnames/
