For me, it really helps to look for patterns. Are there measures or even sections that are the same as others? Study the song, see what is the same, what is repeated. It helps to know that once you learn one section, phrase, or measure, you know it in other places of the song.
For instance, it would be difficult if in everyday conversation, instead of speaking phrases and sentences, we spelled everything out. But we often 'spell everything out' in music instead of speaking in sentences and phrases.
Take 'Jingle Bells' as an example. When I look for similarities, I see that the first and third measure are the same. The first two measures are like one sentence and then the third and fourth measure are another - they're very similar, but with slightly different endings. Then, if I look further, I see that the third line, measures 9-12, are the same as measures 1-4 ... with the exception of the last note in measure 12.
By looking for similarities and repeated patterns, it's easier to not only learn the piece but to memorize as well.
We often have band music that I am required to memorize -- and this helps a lot. Also, the more you memorize, the easier it gets. I was horrible at memorizing before, but got better out of sheer necessity!Jingle Bells Memorization