There is no "one fits all" procedure. What you want to do is arranging: cutting out parts, changing where notes are to fit the instrument or your hand. Arranging was and is very commonly done by many composers and interprets, especially with orchestra scores. Busoni arranged many Bach pieces from organ or orchestra to piano, and added many things that where not written, though gracefully. You have a full range of piece modification from arranging, transcript, to write a fantasia. What you are looking for is the simplest of them: arranging.
Bach and his peers were arranging and improvising, rearranging a lot, so "he" would encourage you to do so.
A good start is to analyse the piece and spot themes (melodic, harmony, rythmic, etc), variations, harmony progression, and remove parts that are dispensable in your opinion, while avoiding cutting in the middle of a sentence, and make sure that the new harmonic progression is acceptable. Analysis is also very good and can help you understand better the piece and remember it formally.
If you're refering to BWV565, the piece is a lot simpler than other Bach pieces such as BWV1080 or BWV1079, so it's rather a good one to start arranging.
You may start arranging without too much analysis: just jump from the end of one part to another, and evaluate if you like the result, and if it makes sense.
As for the "organ to piano" arranging, just play what you can and skip or change the octava of what you can't play easily; if it's already doubled, just drop the note.
At last, if you want to add new elements and improvise from the piece, just do it, you may want to try to do something like Bach would do, but it's not an obligation. Understanding and analyzing how an author is writing can take some time, but it's useful to know that in order to write à la manière de.