Well I agree with practice pracitice etc.Keep playing the same tune over and over. But break it up to learn it, learn the first half of a tune. If it is Irish perhaps do the first part, then as you go on, try testing your self and make yourself not look at the notes, even though they are infront of you.
It does help to if you hear other people play tunes alot. I have learnt a few tunes entirely from sessions, I have never seen the notes. I have got these tunes by hearing them so much and then sitting in the background quietly trying to pitch the note on the instrument I am playing, then gradually it clicks in.
It is not something that comes to most people straight away, but once you have it, it just clicks.
It is like learning the times tables pigeon/parrot fashion really.
Ella