If you are buying via mail order the salespeople are usually good at guessing your Irish size based on your American. If you are not in a hurry, most merchants will allow you to send a tracing of your foot for a perfect size match. But the best way to be sure a good fit is to buy them locally.
A well fitting shoe will feel a bit tight at first. The leather will stretch plenty with wear. If possible, do not buy a shoe that feels like a perfect fit. It will likely stretch enough that it will be too loose. Of course, a shoe that is even a little too big is not worth buying.
Be sure the shoe fits before dancing in it. Once it is scuffed it is un-returnable. Try them out on first on a carpet.
STRAPS: Some come with holes already drilled in them. Ignore this and fit the strap yourself. Measure it while standing up and while pointing your foot. It should always be snug. Anticipate that the strap will stretch almost immediately. Make it a little tight and do not cut off to much extra strap in case you need to cut another hole later, You may need a different hole for socks and tights.
Breaking-in New Shoes