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There's a Piano piece by Steve Reich called piano phase, in which the same notes are played on 2 pianos (usually by different people), but over time, they shift out of phase with each other.
Here's a video of it being done by one guy on youtube:
I imagine it's extremely difficult, but how would you go about learning to play out of phase in such a way?
What make's Reich's piece difficult, is how he specifies the phasing. For example, there are portions of the score where you need to be exactly 1/16th note out of phase with yourself.
Self-phasing is something I have practiced for quite some time, and indeed, it does take a while to learn. However, such practice / skill allows you great freedom through improvisation as well as some very interesting syncopation.
If you're starting from the absolute beginning, then I would suggest becoming very smooth at transitioning between rhythmic durations. For example, put on a metronome at 44bpm or something equivalently slow. Next, begin with a whole note (four beats) and repeat a few times, then move to half-notes, triplet quarters, quarter-notes, eighth, triplet-eighth, sixteenth, quintuplets, etc etc. Practice moving between them staying exactly with the beat.
Once you have mastered that, apply the same technique while keeping one hand constant with the metronome while you accelerate with your other hand exactly with the beat. Next alternate hands.
Really, the trick is being able to multitask.
Quite simply, when you have mastered speeding up and slowing down with the beat, do it over or independently of the beat. If there were measures, you could think of it as being "over the barline." Obviously, alternate hands.
Once you have mastered this task, take it a step further by only tapping on beats 1, 3 or 2, 4 (I'm a fan of 2, 4 personally for jazz reasons.) Once you can arhythmically swing on 2, 4, then you know you can have some fun.
If you want to slow down / speed up at a specific rate, then that will need to be practiced specially - the difficulty really lies in how well you understand conceptually what needs to occur kinesthetically in order for your hands to create the desired phasing effect.
