Learn the basics of music pitch notation. All western music is played on a staff, a series of five parallel horizontal lines used to indicate pitch. The pitch is determined by which line or space of the staff a note head (small, round symbols, usually attached to a fal) is sitting on. The higher the note head is on the staff, the higher the pitch.
Some pitches will sit just above or below the staves. In this case, they may have small lines drawn below and/or through the note heads. These are called "leger lines" and have the effect of extending the staff.
Familiarize yourself with the grand staff -- two lines of staves that are played at the same time, one with the right hand and one with the left. The right hand usually plays in the treble clef, whose notes are (from the bottom up) E,G,B,D and F on the lines and F, A, C, E on the spaces. The left hand plays in the bass clef, whose notes are E, G, B, D, F on the lines and A, C, E, G on the spaces. If there are leger lines, the lines or spaces follow the alphabetic pattern down or up. Note that the musical alphabet goes as far as the letter G, then starts over at A.
Sit with proper posture. Sit upright, but relaxed on your piano bench, positioned at the center of the keyboard. Lift your hands and rest them on the keyboard with the elbows hanging below, and always strive for a sense of weight in your arms, lifting them just as much as necessary to play the notes. Curl your fingers so that your thumbs can reach the keyboard comfortably. Always relax your shoulders.
Discover where the notes are on the piano. If you have a full piano piano keyboard with 88 keys (all natural pianos will be full), the first note on the leftmost bottom of the keyboard will be an A. Regardless of the type of piano, the most important note for a beginner is located in the center of the keyboard: the middle C. The middle C is a white key located just to the left of the center-most set of two black keys. Every other key that follows this pattern on the keyboard is also a C, but in a different octave (meaning it will sound similar, but lower). The middle C appears at the first leger line below the treble clef staff and the first leger line above the bass clef staff.
Operate the pedals with your right foot. Rest your left foot and press your heel to the floor and use your foot as a sort of hinge to depress the pedals. The piano has three pedals (electric pianos might have fewer) used to create different musical effects. The pedal on the right is called the damper pedal, and is used to give the piano a more sustained, echo-y sound. The middle pedal is the sustain pedal. This will sustain any pitches that are played at the same time the pedal is depressed, but no others. The leftmost pedal is the soft pedal. This pedal is used to soften the piano's overall volume.