Exhaustively.
These days I delay going to the piano a lot (I was not always like that). This means that I will work on the score far more time than actually at the piano. By the time I actually get to play a piece, it is often memorised (not always though).
Yes, I can name all the chords, progressions, intervals, etc. When I first started doing this it took a while, but now it is second nature. It followed the smae kind of progression as learning a second language. Now I am quite fluent on it all.
I often liken the process to making a film. Just like the actual filming is usually quick, so should the learning of piece at the piano be. In a film, the director will do a lot of planning, all the scenes will be done in story boards first, etc. The scenes will be filmed not in sequence but according to production constraints. So careful planning is mandatory.
I consider analysis the planning stage. If you do it right, learning/practising the piece at the piano will be quick and enjoyable.
Best wishes,
Bernhard.