Piano Forum

so necessary. But I have recently started playing again and I imagine it is a skill I should pick up.

Well, I wouldn't say it's a necessary skill or technique, but I do it just because it's easy to read the music and sometimes work out some technical problems when I'm not at the keyboard. 

At the very least, it helps me remember a given piece of music, which is the way I prefer to play repertoire.  (That is, I prefer to just play music I know or have memorized, just because, while it's difficult to accumulate a lot of repertoire this way, I don't really like sight-reading at the keyboard....that's more an aide-mémoire, which is unfortunately sometimes required, but one sometimes uses these little crutches.)

If anyone would be so kind to illustrate this going over an example I plan to start studying Mozart's Fantasia in D minor K 397 soon.

That's an excellent example:  so, for me, I'm hearing the broad harmony from Dm and the minor plagal cadence, then at the final bit, in D maj, I'm mostly looking at the LH figure and remembering the melody.

If I were first learning the piece, I'd probably do some bits of work on the octatonic-based (dim W-H) scale bits, and if I felt fancy, try to imagine running those bits in thirds at the keyboard.  Maybe just try playing around with it by reading if I had a bunch of spare time:  you know, maybe transpose the piece or try to imagine some purely mechanical exercises I could do inspired by the piece.  Or, do some metronome-style rhythmic work, in a similarly abstract fashion.

There's really no limit to what you can imagine just reading an arrangement or score:  even better if you have a pencil and eraser. 

Of course, this presumes that you already know how to read, and how to play, and are familiar with your own technical or musical challenges.  Otherwise, reading out of a score away from the keyboard might be not meaningful. 

I don't know how to answer your other questions about the optimal length of the piece and so forth:  it's just a habit, really, when I have a few minutes to spare waiting for something or other.