What are the basic warmup practices and exercises for piano playing?
Generally, warm ups on the piano are very similar to things you might do on other instruments. Playing through scales, arpeggios, chords, or Hanon exercises are all traditional warm ups. These exercises are basically to get your fingers moving and get the blood flowing.
Other people, in the interest of warming up, will just run the hands under some hot water for a minute or two to heat them up.
Personally, I don't really feel the need to warm up at all. My hands will warm up in a few minutes from playing anything, so I'd rather spend that time actually practicing something. This is not to say that I don't practice scales and arpeggios. I just don't warm up with them.
I don't warm up when I play the piano, but I have several exercises that I go through to help with various parts of my playing.
These two are the main two I use.