I had a friend who did it to his Toyota Paseo, which is probably comparable in size and construction to that Civic. I think it was pretty close to the same year, too.

To do it, he literally stripped the interior out of the car from the seats back. All the carpet, headliner, door and wall panels, seats, seatbelts... everything was removed except for the dash. Then he spent a ton of cash on dynamat and covered every available square inch of metal with the dynamat, from firewall to tail lights.

It was a *HUGE* amount of work, very expensive, and in the end, it produced a noticeable improvement in the overall acoustic damping of the car, BUT not a "huge" amount. The car was modern enough so that the amount of acoustic damping supplied at the factory was pretty sufficient. So upgrading to the dynamat, even after all that work, didn't produce as much of an improvement as he'd hoped. He said he wouldn't do it again after that experience.