My procedure for a new piece is usually as follows:
1) read entire work three times, significantly under tempo, observing as much as possible re: phrasings, character, harmonies, technical obstacles, possible fingerings, climax, structure
2) careful work in sections (one or two each day), with more detailed work on phrasing, fingering/redistribution decisions, experiencing mood, internalizing of material. It goes without saying that all rhythms and pitches must be accurate throughout this work, otherwise it is wasted effort. If you cannot do this, choose a smaller fragment and/or slower tempo. Re: dynamic, articulation, tempo markings - always be asking yourself "Why?" Why is there a crescendo here? What would be the effect if it were the opposite? Work to convince yourself that each indication that the composer gives MUST be so, because these indications are an organic part of the musical material, not an addition.
3) eventually, you may decide to test whether it is memorized. There are several ways to do this other than public performance, which include playing slowly (the muscle memory has a more difficult time engaging, and so it gives a more accurate assessment), hearing mentally and "taking dictation," copying the score from memory, playing the LH alone... etc.
In summary, all work should be directed toward a greater musical comprehension of the piece, a more vivid sound image in the mind, and an impeccably accurate realization of this internal image.
Best wishes,
Jean-Baptiste Morel