Puncture holes in the base of the plastic container with a hammer and nail. Space the holes about an inch apart all over the base of the container.
Tear up old paper into small pieces and place the pieces in a bucket. If you are using newspapers and junk mail, discard any glossy pages as these are not safe to burn in your fireplace.
When the bucket is full of torn paper, or you have used all the old paper you have, pour enough cold water in the bucket to cover and saturate all the paper.
Wear rubber gloves and take the bucket of paper, plastic container and a brick to your sink. Place the container in the sink and place a hand full of soggy paper inside it.
Take the brick and press the soggy paper in the container down hard with it. Apply pressure at a 90-degree angle without wiggling the brick. You are aiming to press most of the water out of the paper so that it drains out of the holes in the base of the container.
Add another hand full of wet paper on top of the first layer and press it again with the brick.
Continue in this manner, adding layers of wet paper and pressing it down with the brick to squeeze the water out. You will not be able to get the paper completely dry, but press as much liquid out as you can at each stage.
When the container is about half to two-thirds full of paper, turn the brick-shaped "log" out by turning the container upside down and tapping on its base. Repeat the process to make additional logs until you have run out of paper.
Leave the logs to dry out in the sun or any warm, dry place. Depending on the climate, it may take weeks or even months for them to dry all the way through.