First, let's start by discussing a few of the benefits to memorizing music, the greatest being that it will reduce nervousness. If you know what you are doing, there is significantly less chance for performance errors. Any of us can tell the story of the three bears with little hesitation because we know the story so well. Even if we never told it before, we could improvise the story and touch upon all the key points. We could even loop back around if we miss an important fact. Music is the same. If we were to deliver a speech in front of a crowd of people and we didn't know very much about our topic, we may stumble and stutter a lot, but, if it is a topic we are passionate about and have familiarized ourselves with, chances are we will be successful at getting our point across. No matter how good our technique is, if we don't intimately know the score we are weaving to the listening ear, our tone will belie the the perception that we know what we are doing because it is easy to hear nervousness in someones tone or their lack of articulation.
When our notes are committed to memory, it frees us to be aware of the dynamics of the room or the listeners. I have often found myself playing out a transparent charade of pretending I was taking no notice of the room because I was feigning to be absorbed in the music. In truth, I was running on motor memory and had no idea what I was doing and I was hoping not to hit any bumps in the road.
If you are playing a hymn for a church service where a congregation is singing, you are more in tune with what they are doing and how what you are doing affects them if you know the hymn well. You are more apt to be creative with registration, dynamics, embellishment, re-harmonization, controlling the tempo, breathing and controlling the ritard of the congregation. We know when this happens, likewise, we know when it doesn't. As an organist I am better able to execute registration changes on the fly and with confidence when I know my score from memory.
Being unencumbered by the page frees you in technical ways, too. It frees the eyes to watch the hands so you can better execute fast passages, leaps or grabbing stops. When you are arriving upon a fiesta of notes or a patently impassible passage and you are besieged with nerves, a staccato of thoughts or worse - total thoughtlessness, you may be sitting there consciously hoping not to interrupt the luck of rote memory. Having a score properly memorized will eliminate most of those barriers.
There are many different methods of memorization which people employ. None are better than others and some of us are better at one method more than another but, combined, you will be amazed at what you can accomplish. Here are mine:
1) Repetition, automatic pilot, rote, muscle memory. I consider this method a shortcut to disaster, an unrivaled opportunity for making a fool of self. Consider tying your shoe; You don't have to think about under, over, through; you just do it and can even carry on a conversation at the same time. Any time you have played a piece over a hundred times to the point where you can just play it from "memory" is convenient. You may think you know the piece but when you get nervous or if you slip up, it is often impossible to recover especially if it sends a nascent wave of panic through our thought process, dooming the rest of the performance. Too many things can distract our minds which will mess up what the muscle memory of the hands are doing. It can even be a simple miss-fingering of a passage. Most often it is our own mind getting in the way and we will be judged by a brace of listeners that our musicianship is lacking or called into question when all along it was muscle memory derailed enough to open the door to increasing thought.
2) Memorizing away from the keyboard. This is the first thing I do with all scores, new and old. First I analyze the structural features of the music, taking note of modulations and chord progressions. I focus on difficult passages and landmarks of the piece. I try to hear it in my mind's ear before I play it with my hands.
3) Having a good ear. Not simply playing by ear, but knowing intervals. Knowing what a fifth sounds like and its relation to other pitches, knowing how common arpeggios sound - intimately. Having a few years of solfege study can help tremendously. I know that "Blue Moon" starts on the 5th and my ear tells me the next pitch is a 3rd. Back up to the 5th, a drop down to the 4th, then 5 6 5 5 4 5, etcetera. In classical music, say you are studying a fugue and memorizing it away from the keyboard, you know that the theme may start on a third, then when the second voice comes in, it starts a fifth higher in a new key on the third, then the third voice comes in a fourth above that on the third. You don't necessarily have to memorize every single note, but if your ear hears it and your solfege skills can tell you what the pitch is, you will know where to go or be able to pick up the piece at any point in the score.
4) Understanding chord progressions and sequences of chords. We all know the most common progression in standard repertoire is the I vi ii V. There are thousands of songs which have that progression (such as Blue Moon or Heart and Soul). In most music, ii usually leads to a V7 and V7 usually leads to a I. In classical music it is much the same but sometimes the ii V sequence ascends or descends in whole steps or maybe a V7 may not even head home to a I. Maybe we will land on a I but the composer, Bach for instance, will turn that I into a V7 or a i, starting an episode in a whole new key. Paying attention to the landmarks as I mentioned before is important here. Some composers will throw in a diminished chord out of nowhere while other times the composer will add a few bars of modulation to set up the next sequence. It is important to know where these surprises and deviations are and what they follow. The same thing with difficult passages. If you don't know where you are coming from, you could miss where you are going. There was a leap in a Chopin piece which I consistently missed. The reason was because I was so concerned about hitting that leap, I threw away the scale and arpeggio which lead up to it. By the time I reached for the leap, I had no momentum or control of the notes nor even my hand. Consider a high diver. The most important part of his dive is the set up. He finds the proper position on the board and he executes a few jumps in place to gain both momentum and to establish his balance so that he has power and alignment, then he makes his leap.
5) Part of number 2 and 3 is to memorize the intervals and how the melody is built over the chords. You don't have to memorize the entire piece note for note. Having a good grasp up upper and lower neighbors, passing tones, scales, patterns and arpeggios will allow your ear to be able to hear what is going on and translate your vision to the notes on the keyboard or a page in your mind's eye. It is truly liberating when you can envision the sheet music and read from it in your head. This is not the same as having a photographic memory. It is a combination of ear, sight, motor, analysis and knowledge; all coming together.
Even by utilizing all the aforementioned techniques, a performer may still experience memory slips but they will be better equipped to handle the situation and recover. I was playing a Bach Toccata once where every two bars the music repeated the same phrase but in a new key because the one chord either became a V7 or a ii or i. I got lost and subsequently trapped in sequence after sequence of wandering aimlessly with the same pattern. Luckily I knew what the beginning notes of each section was and when I got back to a one chord I picked up the theme and continued. Most of the people in the audience didn't know that I was jumping all over the score but a few organists commented that they knew that that was not how the piece was written. To my credit, they didn't know what was wrong because I was seamless in my wandering around the keyboard. Everything sounded like it was woven together and what I intended.
Additionally, once I have a good grasp of a piece, I may fool around with it. I will play certain sequences in different keys, throw in arpeggios and scales, re-harmonize it, jazz it up, throw in some blues; In other words, make it mine. After that, I will make a lead sheet version of the music. I can reduce five or six pages of music down to a single sheet. I will then learn the piece bar by bar and use the original score for reference only. I learned Widor's Fifth Toccata off of a lead sheet. The chord progression is very simple and predictable and the pedal line is easy to remember. I simply wrote in the first note of every beat and the accompanying chords. Since the right hand arpeggios are based upon the chord, I didn't need to write them out. Attached is an example of what I wrote up.
The other beautiful aspect of employing all these methods of memorization is that the piece can become your own and you may be less apt to play it the same way twice. You can recover from flubs, play with more expression or musicality and probably most important of all, not sound like everyone else. After all, how excited do we get when we hear somebody do something different to a piece that we've heard exactly the same a hundred times before.