If you're new to Irish music, it may seem strange to you that most traditional players learn tunes by ear, let alone that there are lots of excellent players out there who don't know how to read music. The very idea of doing without the dots and lines is enough to throw some people, especially classical players, into a panic. It somehow violates their conception of what learning music should be like, that you see the symbols and reproduce them and that's that. But there's a lot more to Irish music than that. Nailing the exact notes with surgical precision is all well and good, but what matters a lot more are the things that can't be written down. Learning by ear helps you to understand the large-scale structure of your tunes, which allows you to play around with the details. You can also learn tunes faster by ear and remember them more clearly, since you aren't putting the music through the filter of written notation. Learning from sheet music is like finding your way around a house by looking at a floor plan. Useful in its own way, of course, but when you learn by ear, you're wandering from room to room inside the tune, opening doors and peering into closets, finding your way around it. Your experience of the music is more direct and intimate.
Think about it: you probably have a whole pile of songs you can sing at the drop of a hat: nursery rhymes, pop songs that were current when you were in high school, things like that. It's your musical baggage. Now it's highly unlikely you got any of these songs by poring over sheet music till you got them note-perfect. More likely you got them from listening to your parents, your kindergarten teacher, the radio, or a tape or CD. In other words, you picked them up by ear. This is exactly the way to learn tunes. There's nothing magical or mysterious about it - in fact, you already do it. The only difference now is that you're going to take the extra step of playing the music on your flute, rather than just singing along when it comes on the radio.
Start by listening to the tune a lot, maybe fifteen or twenty times. Get to the point where you can sing the melody without trying. This is the most important step, so take all the time you need. If you catch yourself singing the tune without thinking about it, you're definitely on the right track. All you have to do then is to put it on your instrument. So sit down with your tape recorder (or a patient friend who knows the tune) and work through the tune bit by bit. Take it in bites as small as you have to. Three or four notes at a time, maybe. And again, take as long as you need to. It's going to take a while at first, so be patient and let yourself learn. Above all, don't stress out, just relax, have fun with it, and play. If you can get just the first three notes of a tune, that's enough to build on. You can go on to learn the next three notes, so you know six notes. And then you learn the next six notes in the same way. And then you have twelve notes, which is two whole measures of a jig. So then learn the next two measures the same way. The process goes on like that, as slowly and incrementally as you need it to go.
If you come back the next day and can't remember bits of the tune, go back to where you got it from (the recording or patient friend) and work those bits out. Play through the tune five or six times. It should stick with you pretty well, assuming you laid a proper groundwork by listening first.
Much Irish music on commercial recordings is played really fast, and you may have a tough time picking up tunes from them. If this is a major problem, you might consider getting a tape recorder with a half-speed control. The Marantz brand seems to be pretty popular. Slowing a tune down to half-speed will drop the pitch an octave - if that's distracting, there are computer software applications, such as CoolEdit, that can slow a piece of music down without changing the pitch. I must say that I've never used either one of these tools, though. With practice anyone should be able to pick up tunes at speed without too much difficulty. And practicing costs a lot less than a fancy tape recorder. The only tools that are absolutely required are your instrument and your ears.