A friend recently posed me this question:
"I have an 11 year old student who plays crazy by ear. She picked out a lady gaga song almost perfectly in about an hour. . . any thoughts on how to help her better this amazing skill?"
One of the most important parts of learning a song by ear is recognizing the chord structure around the song. If you can figure out the chords behind the music, you don't have to work as hard to figure out each individual note in the song (most notes will conform to whatever chord is emphasized). Instead of trying to decifer 5 or 6 notes at once, you only have to worry about one or two that are outside the chord structure.
There's many methods of notating and understanding chords (I prefer the Nashville Number System), but there are lots of other choices. Here's a great book on understanding and identifying chord structures:
Listen, Listen, Listen
It's simple: the more you listen, the better you'll get. If you don't have it yet, download spotify and start listening to as much music as possible (note: I'm a firm believer in buying music, but it just makes sense to stream songs that you'd never want to have on your iPod).
Get a Practice Trainer
I remember when I was first trying to work songs out by ear with a CD player. I felt like I spent more time rewinding and trying to find the correct place than working on the song!
There are several options now for practicing songs at a slower tempo. My personal favorite is a mac-only app called gassistant. It's free, and it does a great job of looping and stretching audio for practice.
If you don't have a mac, you can opt for either a standalone solution like the MP-VT1 Practice Trainer, or search on your app store for a practice trainer. I found several on my iPhone's app store that cost less than 10 dollars and did everything I needed.