The Hanon method, a complete method for developing virtuosity created by Charles-Louis Hanon is a bible among pianists. These exercises isolate each finger to develop strength and independence. With 60 total exercises, pianists develop strong finger independence essential to the improvement of playing technique. Practice each exercise slowly at first, at a rate of 52 beats per minute, then accelerate to the recommended tempo listed for each exercise.
The five-finger drill is a basic drill requiring very little piano ability. Start with the right hand on middle C. Keep each finger on top of the white keys so there is one finger per key on C, D, E, F and G. Then, slowly lower the thumb to play C without moving any other finger. Continue doing this with each finger and then play the same notes with the left hand. This exercise will help you develop the ability to move specific fingers completely independently of other fingers.
The Hanon method comes with a complete list of major and minor scales coupled with the correct fingerings. Use the fingerings included with each scale to develop your ability to move quickly across the piano. The fingerings serve a crucial role since they train the fingers to play commonly used patterns in music. If you have trouble playing scales hands-together start by playing each hand separately. Once you memorize the pattern for hands-separate, slowly play the scales hands together. Even if it takes you five seconds per note, you will eventually develop the skill to play scales quickly.
Arpeggios are skips on the piano that outline chords. Each note of an arpeggio will be a third followed by a second for seventh chords and a fourth for triads. Learning to play arpeggios, without looking at the keyboard, will help you improve your sense for the keys of the piano. Aim to learn all your music without resorting to looking at the piano for visual cues. This will greatly increase your familiarity with the instrument and improve your ability to sight-read.