Memory is a complicated stew of ALL the input your senses receive plus your inner mental environment: not just what your fingers are doing, but body position, lighting, what your eyes see, background noise, emotional state, even time of day as it relates to your fatigue factor. Memory is a physical process, not a mental one. It's a reliance on automatic movement (cerebellum) rather than actions your mind (cerebrum) directs. That's why you will never forget how to ride a bike, but you can't remember an address or exactly what was said in a conversation. That's also why music memorized at home is sometimes difficult to play by memory in a different setting: everything is different about the performance except the notes you're playing, so the new input distracts you from being on automatic, and puts you in manual mode. Our minds take in vast amounts of information while we're performing a piece, only a fraction of which is the music you're playing!
By mimicking as much as possible the conditions under which you'll be playing your performance. By being aware of such small things as where your eyes are focussing, your posture, even ambient light. By practicing with your eyes closed to lessen other input. By putting as much color in your music as possible to increase physical input, such as staccatos, crescendi and fluid body movement. By working on passages in their wholeness of complexity rather than first trying to remember words, then melody, then entrances. The brain can handle it all, and the more it has to handle, the more clues it provides itself. By listening frequently to recordings of your pieces for the bigger picture. By practicing accurately, and consistently.
Your brain begins to memorize from the very moment you begin sightreading. It's physical muscle memory that allows you to play faster after you've practiced a section a few times. As that process continues, we call it progress. It's actually your memory at work. "Memorization", that big scary word, simply continues that process without focussing your eyes on the music. Little by little, use the music less. Use your ears more. Some people find they can visualize the page. Others remember specific fingerings or harmonies here and there. There are many, many small clues in the music as you practice, if you train yourself to be aware of them. Awareness is 90% of the battle. The other 10% is practicing with accuracy from the very beginning. If you practice with wrong notes, they'll be wrong, and therefore distractiosn, in your memorization process too.
The brain constantly seeks to integrate and chunk information into larger and larger packages. A slip often occurs in a spot you haven't paid much attention to, which is actually pivotal to getting into your next chunk. It might be a left hand bass note, or a slightly different fingering in a run. Don't be discouraged if you have a slip, it doesn't mean you've forgotten everything that follows, rather that you've lost the key to the next door. Retrieve the key, and you have opened the door to the next big chunk. Differences in environment from practice to performance, heightened attention to spots you've usually ignored, and errors in playing can distract you from the smooth automatic process into your manual mode, which requires too much thought!
Start memorizing from the end of the piece. Find a comfortable spot a few lines from the end and play. Play several times. Look away from the music, and then get it off the stand. Don't even have it there. If there is a spot where you stumble, open the music and mentally analyze the problem. Section practice the spot, working gradually backwards. When you can do that, go back a few more lines and repeat the process. Find similar passages in the piece and play them one after the other, memorizing the differences as well as the similarities.