Boiled, most likely. Up until the 20th century most Irish peasants cooked on open hearths, in pots. It's one reason why soda bread is popularized in Ireland the 19th century --- soda bread rises by chemical leavener, and you can therefore cook it in cast iron pots or on griddles heated over an open flame. No oven, so no baked potatoes or casseroles. You can roast potatoes in hot ashes, but I'm not sure if this would have been a popular method. The Irish tend to favor floury, thin-skinned potato varieties. So yeah, boiled in water or milk, stewed with meat, or mashed with greens (c.f. colcannon). That's about it.

Bon Appetit actually has a decent article on the history of Irish cuisine that goes over some of this, but basically they got by on potatoes and milk.