Can you place your hands over the keys so that they are ready to play, but without actually playing, without tensing/clenching the fingers, hands and/or wrists? If not start there. Explore how your hands feel when they are soft and free from tension, vs when they are not, and learn to recognize the difference. If you have had tense hands for a long time, you've likely learned to block out/ignore the feeling in your hands and forearms that signify that they are tense. But that feeling is still there, you just need to practice "hearing" it again, so listen to your body and compare to how your hand feel when they are just relaxed.
Second thing, once you are getting better at the above, is to see if you can maintain the hands in this soft state when pressing notes. Of course, the finger holding down the key needs to be doing something, but check if the other, non playing fingers are tense. They should be free from tension. Don't forget the thumb! It's a common culprit.
Ideally, you should find a teacher to work on this stuff with, since there is a lot that can go wrong if you try to work from written descriptions. Source: this is what I did when I started retraining my hands to be more relaxed and it was no bueno.