I like using the word 'ease' rather than relaxation... The problem with trying to relax is that it's hard to say how far is too far - it can lead to being too lax. 'Ease' better captures what we're after - we're expending effort, but it's not hard.
So I just try to always achieve that feeling of ease, keeping an eye out for unnecessary tension, which is an indicator that I'm doing something wrong. If you have a digital piano, try playing it silently with the power off, which makes it easier to focus on the physical sensations.
Also see if you might have to improve your posture at the piano. Imbalanced posture is a sure way to introduce tension in your playing. What Every Pianist Needs to Know About the Body is a good book.
Mental stress can also induce tension. A forceful mentality (like forcing yourselves to play faster) tends to result in physical tension. Instead try attaining accuracy and ease, the speed will come naturally once you've got that kind of confident control.
Another thought, sometimes we sabotage our efforts by overanalysing the physical motions. We've already know how to do the physical technique, but for some reason we don't trust ourselves in playing it. The conscious mind begins picking apart details like the motions of our wrists and winds up just interfering with the process, when it ought to be left to the subconscious mind. A useful remedy for this is to focus your attention on the sound your producing, leaving the physical motions to the subconscious. The more you improve the more you should trust your subconscious to handle the details.