How to program a new transponder key?

I'm sorry but programming a transponder key for a 2004 Honda Civic typically requires specialized equipment and training. I would recommend visiting a professional locksmith or a Honda dealership to get this done. They will have the necessary equipment and expertise to properly program the key and ensure it works correctly with your vehicle's immobilizer system.

I found this that you can try:

Transmitter Programming

Storing transmitter codes:
The codes of up to three transmitters can be read into the keyless receiver unit memory. (If a fourth code is stored, the code which was input first will be erased.)

Note: It is important to maintain the time limits between the steps. Make sure the doors and the trunk are closed.

1. Turn the ignition switch ON (II).
2. Within 1 to 4 sec, push the transmitter lock or unlock button with the transmitter aimed at the receiver in the multiplex control unit behind the driver's side of the dash.
3. Within 1 to 4 sec, turn the ignition switch OFF.
4. Within 1 to 4 sec, turn the ignition switch ON (II).
5. Within 1 to 4 sec, push the transmitter lock or unlock button with the transmitter aimed at the receiver in the multiplex control unit behind the driver's side of the dash.
6. Within 1 to 4 sec, turn the ignition switch OFF.
7. Within 4 sec, turn the ignition switch ON (II).
8. Within 1 to 4 sec, push the transmitter lock or unlock button with the transmitter aimed at the receiver in the multiplex control unit behind the driver's side of the dash.
9. Within 1 to 4 sec, turn the ignition switch OFF.
10. Within 4 sec, turn the ignition switch ON (II).
11. Within 1 to 4 sec, push the transmitter lock or unlock button with the transmitter aimed at the receiver in the multiplex control unit behind the driver's side of the dash.
12. Confirm you can hear the sound of the door lock actuators. Within 1 to 4 sec, push the transmitter lock or unlock button again.
13. Within 10 sec, aim the transmitters (up to two additional ones) whose codes you want to store at the receiver, and press the transmitter lock or unlock buttons.
Confirm that you can hear the sound of the door lock actuators after each transmitter code is stored.

14. Turn the ignition switch Off, and pull out the key.
15. Confirm proper operation of the transmitter.

Please let me know if it works.