Short answer: they were boiled.

There are a few reasons for this. First and foremost, once you have a pot in which to boil things, it's pretty solidly the most economic use of fuel, and the method to which you need to pay the least attention.

Second, other methods weren't notably available. The majority of 18th century Irish people who lived on potatoes - and they literally did live on potatoes - were very, very poor. They hadn't shoes, they hadn't metal tools in many cases, they often hadn't real hearths in their houses, and chimneys weren't even a guarantee. Frying pans weren't necessarily there. Ovens weren't a thing at all. Grilling, roasting, etc, couldn't easily happen. Steaming, absolutely not.

Third, boiling is the method that best allows you keep the skin of the potato, and the nutrients in the skin were absolutely essential. These were people whose entire food supply for months at a stretch consisted of potatoes, milk, and herrings. This was supplemented in season by wild food, birds, and other fish, but none of those were reliably supplied.

It's worth noting, too, that diets didn't really improve in many areas even after the famines of the mid-19th century. I wrote a previous answer which detailed some of the diet of the Aran Islanders in the late 19th century, which might also be of interest.

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Sources:

Vera. K. Ninez, Household Gardens: Theoretical Considerations on an Old Survival Strategy (1984)

Cormac Ó Grada, The Great Irish Famine