How frequency generator in telephone works
What you are referring to is called DTMF or "dual-tone, multiple-frequency" or simply tone-dialling.



Figure 1. DTMF table. Pressing a button causes simultaneous generation of two tones - the row tone and the column tone. Source: Wikipedia, dual-tone multi-frequency signalling.

Note that the tones are chosen to be not harmonically related.


  When user click number does it convert to signal and send to wire or when 10 digits are pressed then that group is converted to signal and passed to wire?


If you test this on a landline phone you will hear the tones generated simultaneously with the button press and for as long as the button is held. In any case, the telephone does not know how many digits long a phone number will be.