This is for piano. There is nothing original here. It is been known for hundreds of years. I have simply discovered, belatedly, that it works. I am in danger of becoming very boring - as I repeat the same advice!
There are many stories of immensely able musicians that can hear a piece once, play it immediately, and remember it forever. I haven't met one yet. I think it would be safe to bet that few readers of this post fall into that group.
The method below is not revolutionary. It is not exciting - except insofar that something that works is exciting, and it needs patience, discipline, and faith:
1. Study the score to get an idea of the structure of the music, the key, the modulations, the time signature, the rhythms, the motifs and melodies, the harmonic movements ... Also consider when it was written, so what was the style of the time, how were tempo markings interpreted, how were ornaments realized. THese also varied from country to country, between composers, and even with the same composer at different periods.
2. Ideally get an idea of what it sounds like from reading the score. Alternatively listen to a recording or visit a concert (but don't be too influenced by one particular interpretation). If you absolutely must play through it then do so, but don't play through it twice - that is just practicing a semi-random fingering and an interpretation that has not been thought through.
3. Next pick a section to start work on. It does not have to be the beginning. Sometimes learning the finish and working backwards is good. Sometimes it is good to crack the technically hardest part first (especially if you have a performance deadline). Other times some central part will be the most meaningful part of the piece.
4. Now serious work begins. Divide the part you have decided to work on into short sections - short enough that after playing one of these shorter bits half a dozen times you'll be able to do the next couple of repeats without looking at the score. Make the sections overlap slightly, so that continuity is not a problem later. Then set to work. Your aim is to play each small section absolutely note perfect. Go as slowly as you have to to make this possible. Mark in your score any changes you need to make to the fingering. When the fingering is tied down and you have the notes repeat the section a few times. Then move on to the next one. And continue until you have completed your alloted work, or until you find you have lost concentration.
Do the same at your next session. You won't need as many repetitions, and you'll be better able to control the touch and dynamics. When you have a solid grasp you can start to play longer sections.
If you encounter something that is simply too difficult you may need to seek out a study that focuses on that skill, or technical exercises, or devise your own.
5. Proceed in this way until you have learned the entire piece. Continue to work on the musical meaning and the interpretation that you want to give.
I know that this all can seem tediously slow. It is very tempting, especially if you are a good sight reader, to simply play over the whole piece a few times a day until it becomes fluent. But doing things that way you never ever make the piece totally secure for performance, and you never penetrate into its inner secrets.
The slow and methodical method turns out to be the faster way to build secure, performable, and if you want it - memorized, repertoire. It also allows you to successfully tackle pieces that, if you have never worked this way before, appear to be far too difficult for your present level of ability.