i only play trad music, so i don't know how helpful this will be, but it seems to work for me - i've never had a problem memorising a tune...
the first thing i do is look for the structure of the tune. nearly all trad tunes follow the same format: 2 repeated parts (A and B) of 4 or 8 bars. (some tunes have 3 or 4 parts, or longer parts, but the same principle applies). within this, the melody often follows a question/answer style, where either the question or answer will be repeated in each part; for example, the A part of
Drowsy Maggie is:
E- BE dEBE | E- BE AFDF | E- BE dEBE | BABC dAFDthe first bar forms the repeated question.
other times, the same answer from the A part will be used at the end of the B part, so if the A part were subdivided into 4 bars as A-B-A-C, the B part might be D-E-D-C (
Staten Island: see the repeated |d d efge | f d d| at the end). or, you might have the same question with a different answer, but this is quite a bit less common (
Irish Washerwoman).
many trad tunes have a noticable 'low part' (A) and 'high part' (B), and when that happens, the B part often has many similarities to the A part (
Mountain Road: the B part rhythm is nearly identical to the A part).
i should note that i don't spend hours sitting down analysing tunes; the things i described above become obvious very quickly by the second time you heard the tune (at least when you do it often enough).
once you've recognised the structure, it's easier to learn the tune: you know what comes where, and you don't have to relearn the same repeated phrases. at this point, if you're reading from dots rather than by ear, you can probably hum the tune, even if you can't play it through. if i'm learning from dots, i always make sure i know the tune first, by finding a recording (or several) if i don't already know it; if i can't, i usually won't try to learn the tune, although i make an exception for hard-to-find tunes that are played at my session, since i can 'check my work' next time it's played. (i'm thinking of getting an audio recorder to make this a bit easier...)
at this point, if i'm playing from dots, i'll play through the tune repeatedly until it's "in my fingers"; then i'll look away and see how much of it i can play without them. it's important that you really try to do this; if you just play it from the dots all the time, you'll never learn it, or if you do, it'll take much longer. by deliberately playing without the music, you force yourself to remember it. it usually doesn't take me many tries to memorise the tune like this.