Before a piano is tuned, a general assessment is done to look for any issues that would impair playing and tuning of the instrument. No one wants to play a piano with sticking keys, or a sluggish action. So those problems should be identified and remedied as best they can be before tuning. You would also check for broken strings, and loose tuning pins. This is done to insure that the final tuning will remain stable.
Once everything has been verified to be in good shape, the next step is to assess the current pitch of the piano. The A at the 4th octave should ideally be equal to 440hz. If the pitch of A4 is too far below 440hz, say at 435hz, then a "Pitch Raise" becomes necessary. It is necessary because if you tried to tune the piano to A440hz from 435hz, it would result in an unstable tuning because of the rapid change on string tension. Therefore it would only fall to a lower pitch later on and be out of tune again. So, the goal of a "Pitch Raise" is to bring the frequency of A4 just the right amount "above" 440hz, so that it will fall to the desired pitch. Then a fine tuning can take place.
First, the strings are strip muted with felt so that only one string of two and three string unisons ring out. Starting from the middle section of the piano, you tune what is called the "Temperament Octave". The "Temperament Octave" is called that because the goal is for all of the notes in that octave to be evenly divided and tempered. This tempering is done to compensate for the mathematical discrepancies that occur in all pianos because of varying string length. Basically, the entire tuning of a piano is based off of the "Temperament Octave". And every interval relationship within the "Temperament Octave" will be reflected in the Bass and Treble. From there, you can move on to tuning the Treble and Bass. The last step is to remove the strip mutes and tune the unisons so that each note rings out as one whole tone.