How do you communicate if the power grid of the country shuts down?

On short distances, you could talk. On slightly larger distances, you can shout, wave, use semaphores or smoke signals. You can use a battery-powered torch to communicate with Morse Code. You can connect two empty cans with a piece of string and use them as a half-duplex telephone replacement.

You can send letters.

You won't be able to use a telephone if the power grid of the country shuts down for a prolonged time, but in case of a temporary or localized outage, you can use the telephone through a regular landline. These lines are backed-up by batteries and generators, in order to enable emergency calls and some-such in emergency situations.

Note this may not apply to cellular (mobile) phones. Among the non-verbal forms of communication, you could use your body language, or sign language.