My father-in-law asked me to learn to Saint-Saens's Introduction and Rondo Capriccioso. It's been a while since I last prepared any music that was a technical stretch, so my process is rusty. I welcome these occasions. Exercising rusty skills has very often led me to a systematic understanding of what had been a subconscious ability.
Of course, I flubbed it. I began by playing through the section I was working on and choosing bowings and fingerings, deciding where to shift, which shifts would get a portamento, which should be invisible. It was after working on this a bit that I realized that I did not have the music itself clear in my head.
I put down the violin and counted my way through rhythms and runs until I could sing the section with each note clear, from long notes to the fastest arpeggios. Actually, there are still two arpeggios which I need to work through again without the violin to get the timing right.
I also formed the beginning of a habitual error in two places. I'm going to avoid even thinking about those passages for at least eight days in hopes of not reinforcing the habit (eight days being an estimate based on my experience with memorizing vocabulary with SuperMemo).
Having flailed around today and remembered how this is properly done, I get to do it right tomorrow. You start without the violin, and work through a passage. Make sure you know the piece as music, with no reference to the technical issues of rendering it on the violin or any other instrument. The goal is to be able to execute the music in your head in time, with your mind focusing on each note, one after another.
It's all too easy to develop bad habits at this stage as well. The easiest way I know to avoid it is to take the musical aspects separately. Figure out the pitch of each note and the intervals to its neighbors without reference to rhythm. Work out the rhythm of each measure without reference to pitch and be able to execute it in time. Then start combining the two, executed slowly enough to be easy.
Think through the gestures, the slides, the decoration of the notes at this point before speeding it up. I tend to dance while I play, so I link a lot of elements of the music to gestures and other kinesthetic cues.
When you have a physical feel for the music, with each note clear and in its place, start to bring it up to performance tempo. Aim for fluent mental rendition before introducing the technical problems of an instrument.
Then go back over the passage and figure out how it's going to fit onto the violin. Figure out fingerings and bowings, how much bow at what point in the stick each note gets, where to shift, and where the shifts should have portamenti and where they should be invisible. Decide what passages are going to require specific training, either because their complexity makes them unplayable except from muscle memory, or because they touch on a weakness in your technique.
The aim of all of this is to avoid bad habits. Playing a piece of music is almost entirely a matter of habits linked one after another, whether it's slides and trills in a little slipjig or technical virtuosity in a concerto.
And habit formation is strange. It's very hard to make small modifications to a habit, and much easier to replace it with a very different habit. For example, there are several fast passages in my repertoire where my left and right hand synchronization fall apart. They have for years. The habits are horribly ingrained. When I try to fix the synchronization, my focus is necessarily on a deviation from an existing habit, which has very little effect on the habit itself. A very different habit isn't perceived as a deviation from the old habit. It just coopts the old habit's triggers, which is why it's easy to change the interpretation of a whole passage of music, but hard to fix one note.
The whole process of preparing music is an exercise in designing habits, and a bad habit represents a huge loss of time.