Develop and warm up your fingers with a simple finger independence exercise. Place all five fingers of your right hand on the piano. Each finger must be on a separate white key. Most people start on middle C. Depress your thumb and release without moving any of your other fingers. Complete this exercise five times with each finger and then move on to the left hand.
Practice major and minor scales and gradually increase the maximum speed that you can play them with control. Aim for a three-octave scale ascending and descending and use the same finger pattern each time you play. Start at a tempo of about 60 beats per minute and gradually increase the tempo until you can play each scale at 144 beats per minute in sixteenth notes.
Play Hanon exercises to improve your nimbleness. Hanon exercises, endorsed by several pianists including Sergei Rachmaninoff, consist of technical etudes that help to isolate and train individual fingers in a safe and efficient manner. Start slowly and increase your metronome speed until you can play the exercise at the indicated tempo.
Play arpeggios throughout the entire range of the piano. Start on C on the lowest part of the piano. Use your right thumb to play C, your middle finger to play E and your pinky to play G. Tuck your thumb under your middle finger and jump to the next C and continue. With your right hand, use your pinky, index finger and thumb, and then jump with your pinky to the next C.