Purchase a soprano recorder and an instruction book. Spend a few weeks becoming familiar with how to place your fingers to make the various notes. If this is your first musical instrument, read the music theory included in the instruction book carefully.
Select an easy repetitive tune for your first Irish melody. "Molly Malone" is a good choice. The finger placements are easy, the tune both plaintive and lively -- typical of Irish music -- and the subject gives the musician a good look at life in Dublin.
Learn to play the tune at a slow tempo, making sure you have the intervals between the notes correct. Once you have learned the finger placements and intervals, increase your tempo until you are playing the melody at the accepted rate for this particular song.
Acquire a professional recording of your selection. Play along with the recording until you can come in perfectly on the parts suited to the recorder. Try improvising and inventing notes to play around the melody or to add to the recording. Irish music lends itself well to runs and trills, techniques that should be listed in the back of your instruction book or in an advanced book in the same series.
Find a recorder group to join. Experienced musicians will be able to give you tips on improving your mastery of the recorder. Playing in a group will give you the opportunity to play descant or harmony. Many Irish songs are drinking songs or dance numbers -- music meant for good fellowship.