We all know that relaxing your wrist, fingers, shoulders and arms will make your piano playing more fluid and smooth. There are points and steps that you can use to check how relaxed your fingers, wrists, and shoulders are.
Those points and steps could be used any time you are pressing a key while playing the piano:

• Make sure you have good posture. Sit up straight with your feet on the floor and at a comfortable distance from the piano or keyboard.
• Relax the muscles in your arms, wrists and hands.
• Keep your wrists straight and curve your fingers as if you are holding a round object. It will keep your fingers close to each other and minimize the difference in length between them. This way, you should be able to shift your thumb under your other fingers in a comfortable way.
• Short fingernails are a must, as that eliminates noise from your nails hitting the keys.
• When you play a note, make sure it does not alter the position of your hand or the rest of your fingers. Fingers are not supposed to be sticking out or up and should be on top of the keys.
• Your shoulders should be down and relaxed.
• Keep your arm weight down on the key. Relax your wrist so you can move it side to side while pressing on a key. This allows your other fingers, which are not used at the moment, to also be relaxed.

Some useful points on sight reading.

Start with acquiring a strong sense of where your fingers are on the piano. Your muscle memory develops through repetition of finger movements over time. Your fingers can learn how to find their notes without your eyes.

• Feel the keys. The goal of this exercise is to keep your eyes on the sheet music without going back and forth between the piano and the music. Develop a good sense of touch by gliding your fingers over the white and black keys. Your D is between 2 black keys that are grouped together. Your C is before the group of 2 black keys. Your F is before the group of 3 black keys. Place your fingers 1 through 5 of your right hand on C, D, E, F and G and slide them back and forth down the white keys so you can feel the black keys.
• Always sit in the center of the keyboard or piano and in the same place. It will help your body and your hands to develop a good sense of position in reference to the piano.
• Practice your scales, chords and arpeggios without looking at the piano. Repetition is the key.
• Memorizing your keys. Create a mental picture of every key in your head. It should work the same way you would recognize any letter in the alphabet. Visualize those keys on the piano.

Before playing a music piece:

• Look at the time-signature and type of notes that are used throughout the music. Look for rhythmical patterns and changes. Clap and count before you even attempt to play the piece.
• Look at the music-key-signature. Find all the keys that will be affected by the sharps or flats of the key-signature. Using this technique, you can anticipate them. Find all the accidentals (flats, sharps and neutrals that are not part of your music piece key-signature.
• Look for 6th and 7th intervals, as those are the most difficult to identify. Knowing your intervals is crucial in precise note playing.
• Look for patterns and repetitions in the music.
• Look at the direction of the music so you can position your hand and fingers appropriately.

While playing a piece:

• Pick a comfortable tempo. Play easy pieces in a moderate tempo. Play hard pieces in a slow tempo.
• Look ahead, especially when your last note in the measure is a half note or a whole note or a rest.
• Get into the habit of counting in your head or out loud.