Suppose there is a massive black-out and there is no way to communicate via modern day technology, what method will you use to continue communicating?

Do the japanese thing! Bake a cookie and put a piece of paper with your message inside and distribute it to the public! haha this is silly but if you read the Philippine history during japanese occupation to the phils.
they use this method of communication to create a propaganda against japanese colony.
They succeed and this method was only known by the japanese at the end after they being defeated.

Hi !! Pigeon Post ...might be!!! Warm regards-Richard

included drumbeat,fire smoke signals and instruments such as ram's horn....

Effective Communication requires at least one transmitter and one listener / responder.
The ability to communicate is based on both the transmitter and the listener / responder understanding the signals sent between them.
Today our communication is primarily based on voice and data and both of these are based on language.
If there were a massive black-out and there is no way to use modern technology to communicate we would have to resort to old systems of morse code or maybe even smoke signals.
However the efficacy of the communication would be varied depending on how many listeners / responders would understand this language form.

Messengers, pigeons, sending messages by ship or train ( if they existed ) or any transported animals etc.
Many ideas but we tend to depend on technology methods.
Hopefully, it is helpful answer.
Regards, Saeed