Many professional piano tuners and technicians know how a piano is tuned and make it seem effortless. It might seem a bit difficult, but it's not completely out of the question. With practice and experience, anyone can learn how to tune a piano with ease.
A Step-by-step Guide
Before we begin, there are at least 3 basic tools―tuning lever, rubber tuning mutes, and electronic tuner. Open your piano cabinet and remove any extra pieces on the top, so you get as much light as possible. It's advisable to remove the cabinet till the top keys.
Always start from the middle octave, so that we can identify which string needs to be tuned. Place the lever on the first pin and press the key so that we can trace the string to its matching pin.
Now it's time to mute the remaining string(s). When you have the correct string to tune, place rubber mutes over or next to the strings that need to be muted and the soundboard.
Make sure there's no noise while you're tuning it, as the electronic tuner will detect the slightest sound. Place one hand on the lever and one finger over the key, press a key and check the tuner. Move the lever slowly as you're pressing the key again and again, turn the pin in a clockwise manner, so that you can elevate the pitch and counterclockwise manner to turn it down. Don't jerk or overwork the pin too much or else it will loosen it. Your aim is to get the electronic tuner needle to stay as close to the center as possible.
Take out the rubber mute of the other string that is closer to the pin we just tuned. This is where you will try to tune the string with your ear. Try to match this untuned string with the string we just fixed. If your piano has 3 middle octave strings, you need to repeat steps 1 through 4 for the entire middle octave. This is where you can master the art of tuning a piano by ear and not with the help of an electronic tuner.
Now that you've learned how to tune the piano by ear (in this case, the first octave), this can be your reference octave for the entire piano. You will take one string at a time in each set and tune them accordingly. That one string should match the note from your reference octave and then the rest of the strings in the set will follow the first string tuned in the set. You can go up or down the piano, whatever suits you, and adjust the tension in the notes of the soundboard equally.
I would advice you to hire a professional piano tuner, if you've never done it before. Unless and until you are sure about what you're doing, don't attempt to handle it on your own. You should hire someone who has had prior experience, and perhaps teach you a few basic techniques.