What is a typical practice routine for you? Not how long really but how do you like to practice? What approach do you take in learning a new piece?
All these questions about practicing and performing make me wonder if I ought to develop a fancy routine, just to impress you all.
You will be incredibly disappointed to learn that I usually just sit down at the piano and start playing. Someday, my body will give way, and it'll probably take a bit more time to warm up, but for now, I find that as long as my mind is clear, and as long as I'm not playing something with extremely fast finger work, and as long as I wasn't just outside in negative 30 degree weather, I'm fine.
I usually just play whatever I feel like practicing. Often times this happens to correspond with what I need to be practicing, say, for an upcoming concert (that "need" to practice leads me to "feel" like practicing). But even in such circumstances, I often find myself sight-reading different music to suit my moods.
As for learning a new piece, my approach depends on the music itself and the deadline I'm facing. If I'm in a hurry, I learn passage-at-a-time until I've got the whole piece in my fingers. If I've got time (the preferred method of doing things!), I learn the piece very slowly and very carefully. This aids memorization and appreciation of the music itself.
There is one thing I never do when learning a new piece: listen to a recording. Only when I'm ready to perform a work will I allow myself to hear another interpretation. I want the music to mean something unique to me, and I find that when I listen to recordings, I tend to fuse my personal experience with the music with another's.