Well, I may as well disappoint you right now to save you wasting your time reading this whole article, no matter how beneficial it is to the willing reader:
There is no way to learn a song 'quickly'.
There is no way to learn a song 'quickly'.
What does quickly even mean, anyway? Half an hour? Two months? How long is the piece? How many sections does it have? What is your level of notation theory? What chords do you know? Do you even like the song? Have you listened to the original or at least to recommended recordings of it? Do you know all the keys involved? Are you able to use your Internal Piano or are you chained to the piano?
Get the idea?
First advice: Don't even contemplate the desire: "learn a song quickly". Instead, contemplate: "learn a song".
Second advice: Answer the questions posed above and if you come across any unknowns or negative answers, fix them immediately.
Third advice: Read on.
There are two types of song to learn on the piano: with lyrics and without lyrics. If it has lyrics, it is most likely from the beginning of the 20th Century onwards (Jazz & Pop); without, let's say the 19th Century and before (Romantic & Classical).
I make this distinction because: if a piece has words, no matter the era, master them before even going near a piano, before dissecting the piece in any way and before even trying to remember the melody. Why? Because the words will subconsciously and passively 'teach' you the melody, the structure and to some extent, when the chord changes come. These three things are literally invaluable and would otherwise take much longer to acquire if the words were ignored.
I would like to introduce you to a new philosophy. You know about the Internal Piano but now we need to activate and work with the Internal Jukebox! We all have one; everyone knows at least a few songs from beginning to end, words and even instrumental solos, in our mind without needing to hear it. If we want, we can sing or hum along as if we wrote it ourselves when we hear it, knowing every tiny drum fill, guitar pluck and backing harmony.
The interesting thing is that the internal jukebox was programmed subconsciously; we heard those classic songs on the radio in the kitchen, in the car, on our old minidisc players (remember those!?) so many times that even if we didn't necessary like it, we still knew it front to back. If the internal jukebox can learn a song effortlessly and literally by-pass our conscious mind, imagine how quickly it can digest a song with conscious effort!
Conscious effort doesn't mean force, stress or struggle, it simply means we purposefully listen to a song on repeat and make some kind of effort to listen purposefully to the lyrics until we can mumble them to ourselves. Subconsciously, the melody, structure and 'chord change points' will stick. This is priceless knowledge when actually at the piano and beginning to dissect it; I'd even go as far to say it's 90% of the work done.
If no lyrics exist, one is still to internalise the piece, from the original if at all possible, and then adding other versions to see if you like certain interpretations. Simply get to a point that you can play the piece, no matter the length, on your internal piano. Listen everywhere, as often as possible.
If you're sick of it, move away and listen to others you may wish to learn; you'll miss the piece eventually! In other words, the best mind frame from which to learn a piece is: calm, happy and rested. Do what you must to get to this point, then read on.
Dissection. The time has come to chop it up, rip it to pieces, undo the screws, blow it up. You know it so well so you know what the finished product 'looks' like, so do not fear. Be grateful that its on programmed onto your internal jukebox.
For analytical reasons, a composition, no matter its era or apparent complexity, is best broken up into three primary components, each of which being subdivided further and mastered individually both at and away from the piano. In order, they are:
These are in order for a reason because without number 2, 3 is not possible and without number 1, 2 is not possible. Structure is always your starting point (once lyrics and excessive listening has resulted in a new internal jukebox track!)
Lyric-based or not and no matter the era, structure will generally follow some kind of norm which can be modified a tiny bit. This involves some kind of verse (A section) and chorus (B section) alternation and/or repetition. If an A or B section is different slightly the second time it is sung (or third, fourth, ...), add 1, 2, 3, etc. after the letter.
A sample song structure could therefore be: Intro / A1 / A2 / B / A1 / A2 / B / B / C / A3 / Outro, whereby the verse is a little different throughout the song then in some way different again at the end, but the chorus remains the same throughout. A bridge also exists, usually of 8 bars but this is not set in stone.
Awareness of this tiny bit of theory will assist you greatly in working out how the song was constructed.
Once each section has been identified with a letter, dive into the chords. If the piece is of the 20th Century, usually the chords will exist in letter form, such as represented in this image, whereas 19th Century composers generally did not use chord symbols and simply wrote the piece out note for note. Even if this is the case, it is still possible to study the score (or listen closely) and identify the chords as the melody progresses on top. You will make progress in either sight-reading and/or transcribing, both excellent skills.
Before adding the melody, now would be a good time to play along with the piece. Because you have mastered the chords of each section, having already mastered the structure and of course, having the piece on your internal jukebox, this will be fun and surprisingly easy to do.
Then, add the melody! Again, sight-reading or transcription practice being acquired here!
All of that can take place at the piano but this does not mean you do not continue when away from the piano. When listening to either the original in your headphones or on your internal jukebox, say the chords to yourself as the song progresses and mentally acknowledge the sections as they arrive. The more you do this, the easier it will be AT the piano. In fact, it will help you so much, I can't even express it in words.
I already have an article on dissecting a piece in terms of sight-reading difficulties which may interest you.
I hope this helps you to acquire the repertoire you have always desired without worrying about if it's 'too hard' and other such nonsense!
Perhaps you'd like to hear my recent composition: https://soundcloud.com/danthecomposer/the-middle-way