Learning by ear is the generic term for learning without musical notation, there are many different ways to learn and the more of them you can utilize the better. Celtic music has been around longer than standardized music notation and players managed just fine without needing the dots to learn new tunes. Learning to develop and use these different methods will make you a more versatile and adaptable musician. It isn’t something you will be able to do straight away but you will get better as you become more fluent on your instrument.
Being Shown: This is where someone plays through the tune section by section, very slowly, until the learner has mastered the sequence of notes. This style of learning relies on listening, watching and being able to verbally describe the sequence of notes. When attending instrument/tune workshops, this is the usual method of teaching, some tutors will provide notation at the end of workshops but don’t count on it. Take a device to make a recording on (don’t rely on your memory for new tunes).
Listening: Many players learn tunes from recordings (and they record tunes they hear being played) usually through a process of listening to a small section at a time and working out the sequence of notes, keep going until you have the whole tune. There are also apps available that can slow down audio recordings (without changing the pitch) which make this process much easier. (Audio Stretch, Amazing Slow Downer)
Watching: When you attend a session make sure you can see other peoples fingers, having a visual cue to complement listening is sometimes the extra thing you need to help work out the sequence of notes.