I have been playing Debussy's piano works since 1979 or so. Over the years I've evolved a set of principles with which I approach each work. These principles can be summed up as: "follow Debussy in detail where he is explicit, and understand the effect he is trying to achieve overall". More specifically:
Take the articulation, phrasing and touch marks seriously. Everything I've read about Debussy indicates to me that he was a very precise technician, and if he wrote a mark on the music he probably meant it. Debussy's piano music is full of specific and sometimes complex markings. Here are some examples: A staccato mark under a tie usually means to hit the note with a bell-like tone. Rests (contrary to many interpreter's opinions) should be taken seriously. Debussy himself complained (I have to go find the reference) about pianists who roll chords when this is not indicated in the music.
Similarly, take
note timing seriously. Debussy does some
wonderful things with timing variations. Notable
examples: Claire de Lune from Suite Bergamasque,
the ending of Reflections in the Water. There
are some notable apparent exceptions such as the doubling
of the note time values starting at measure 7 or so of
the Engulfed Cathedral: in the Weldte recording of
Debussy playing this piece he plays as if the note values
were not doubled (as do all recordings I've ever heard).
There is a telling story about a time a pianist visited
Debussy and played a Debussy piano piece. At one point
the pianist said "This part is to be played freely,
yes?". Debussy later told a friend that he said
nothing but looked down at the carpet and decided that
this pianist would never tread on it again. So unless
Debussy explicitly says otherwise he probably intended us
to execute his timing marks exactly.
Debussy valued transparency. Leon Vallas explicitly brought this out in his book Theories of Claude Debussy, and I'm sure I've read this in Debussy's own writing. Transparency can be very difficult to attain in the multi-layered piano music of Debussy, and requires great care in how each note is hit, so that notes playing at the same time have their own distinctive character. Dumesnil's tutorial has some very nice exercises that are useful here. One of the most challenging pieces to play with transparency is Claire de Lune from Suite Bergamasque.
Debussy valued shape and flow. This is what I think most interpreters mean when they say that one "smears" sound in Debussy's piano works. The overall shape and flow of the music is of paramount importance. Understanding the shape and flow of a piece at the level of phrase, section, and in total is critical for realizing the power of Debussy's music. Strong use of contrasts, builds and releases occur in many forms including volume dynamics (Debussy's music is NOT always soft), harmonic structures and the interweaving of themes.
Pedal to establish shape, flow, and be sensitive to transparency. Pedaling is one of the most important and least notated aspects of Debussy's piano works and so makes the greatest demand on the understanding of the interpreter. Rules like Gieseking's "the pedal should be held as long as the bass harmony" are clearly inappropriate. I strongly feel that good pedaling decisions can only come from an understanding of the shape and flow that Debussy is trying to attain.
Debussy's music is fundamentally emotional, not picturesque. For me this insight was a real breakthrough: we are taught that Debussy's music is "impressionistic", in that it gives the impressions of various scenes. This is certainly suggested by many if not most of Debussy's titles. But I feel this is very misleading: Debussy himself was hostile to the title "impressionist". Paul Roberts in his book Images makes the point that Debussy had more in common with the Symbolist poets and painters, with their focus on mystery and hidden layers. The power of Debussy's music is that it provides you with a sense of presence, not as if you were viewing the scene but rather as if you were feeling the scene. Notable examples: the loneliness of Footsteps in the Snow, the mystery then power of The Engulfed Cathedral, the energy of Gardens in the Rain. Yes, there are clearly theatrical effects in these pieces that are clearly meant to evoke specific images, but these images are there to provide an emotional experience.
So when I approach a Debussy piano piece, I ask several questions:
What emotion is Debussy trying to attain here?
What is the shape/flow/feel of this piece?
What is the role of transparency?
Since I've taken this approach I've had a much deeper experience with Debussy's music.