Need to program new & reprogram older handsets of Panasonic KX-T7730 telephone system ref time & date and extension names...

You need to set the date and time from the default extension "the programming extension" normally extension 20 or 21. You need to enter system programming mode - refer to user manual, then once set, all handsets should display the correct date and time.

Basically, there are 2 ways of programming the date
and time - the short way and the long way.
If you are using the KX-T7730 phone on a Panasonic
KX-Txx 308/824 system:

SHORT WAY:
From the Switcboard / Main telephone
( ext 101, 10 or 9 ) with the handset on the
cradle/hook:
1. Press PROGRAM 0
2. Enter Date and Time
( The format is: yymmdd,
1 to 7 1=Monday 2=Tuesday etc, hh:mm,
0 or 1 0=AM 1=PM ) see example
3. Press AUTO DIAL / STORE to save your changes
4. Press PROGRAM to exit program mode

EXAMPLE:
If the date and time is 3 February 2010 Tuesday 2:15 pm you will enter as follows:
100203 2 02:15 1

LONG WAY:
From the Switcboard / Main telephone ( ext 101, 10 or 9 ) with the handset on the cradle/hook:
1. Press PROGRAM * # followed by the system
password ( default is 1234).
2. Now press 000 and then SP-PHONE.
Enter the year.
3. Scroll to the month with the right scroll key
(located at the right bottom corner of the phone).
To change the month use the AUTO ANS / MUTE
button.
4. Now scroll right again and change the date and
day.
To change the day, again use AUTO ANS / MUTE
5. Scroll right again and the time will appear.
Set the time.
To change am/pm scroll to it, and again,
use the AUTO ANS / MUTE button.
6. Press PROGRAM to exit program mode and you
are done.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system.
From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle/hook :
1. Press PROGRAM * # followed by the system password ( default is 1234).
2. Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ).
3. Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change.
4. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered.
5. Press PROGRAM to exit program mode and you are done.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system. From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle press PROGRAM * # followed by the system password ( default is 1234). Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ). Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered. Press PROGRAM to exit program mode and you are done.
PLEASE rate / vote this answer if it was helpful.
Thank you.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system. From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle press PROGRAM * # followed by the system password ( default is 1234). Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ). Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered. Press PROGRAM to exit program mode and you are done.

Basically, there are 2 ways of programming the date
and time - the short way and the long way.
If you are using the KX-T7730 phone on a Panasonic
KX-Txx 308/824 system:

SHORT WAY:
From the Switcboard / Main telephone
( ext 101, 10 or 9 ) with the handset on the
cradle/hook:
1. Press PROGRAM 0
2. Enter Date and Time
( The format is: yymmdd,
1 to 7 1=Monday 2=Tuesday etc, hh:mm,
0 or 1 0=AM 1=PM ) see example
3. Press AUTO DIAL / STORE to save your changes
4. Press PROGRAM to exit program mode

EXAMPLE:
If the date and time is 3 February 2010 Tuesday 2:15 pm you will enter as follows:
100203 2 02:15 1

LONG WAY:
From the Switcboard / Main telephone ( ext 101, 10 or 9 ) with the handset on the cradle/hook:
1. Press PROGRAM * # followed by the system
password ( default is 1234).
2. Now press 000 and then SP-PHONE.
Enter the year.
3. Scroll to the month with the right scroll key
(located at the right bottom corner of the phone).
To change the month use the AUTO ANS / MUTE
button.
4. Now scroll right again and change the date and
day.
To change the day, again use AUTO ANS / MUTE
5. Scroll right again and the time will appear.
Set the time.
To change am/pm scroll to it, and again,
use the AUTO ANS / MUTE button.
6. Press PROGRAM to exit program mode and you
are done.

I assume that you want to program the extension names.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system. From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the hook/cradle press PROGRAM * # followed by the system password ( default is 1234). Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ). Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered. Press PROGRAM to exit program mode and you are done.
PLEASE rate / vote this answer if it was helpful.
Thank you.

The side buttons is programmed as extensions
To change the extension names follow these steps :

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system.
From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle/hook :
1. Press PROGRAM * # followed by the system password ( default is 1234).
2. Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ).
3. Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change.
4. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered.
5. Press PROGRAM to exit program mode and you are done.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system. From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle press PROGRAM * # followed by the system password ( default is 1234). Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ). Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered. Press PROGRAM to exit program mode and you are done.
PLEASE rate / vote this answer if it was helpful.
Thank you.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system.
From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle/hook :
1. Press PROGRAM * # followed by the system password ( default is 1234).
2. Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ).
3. Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change.
4. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered.
5. Press PROGRAM to exit program mode and you are done.