While several methods exist to recycle paper, they all follow some plan to retrieve stock fibers from waste paper. Here are details for one method, the Black Clawson pulping system.
Waste paper is dumped into a vat filled with water. This vat, called a ragger, sloshes the paper around to break it up. If white paper is going ot be made from the waste, chemicals are added to the water to dissolve the ink. Large contaminants, called strings and rags, settle out while the finer stock fibers flow into another compartment.
From here the stock gets pumped through a large centrifugal cleaner. This machine spins the stock and water mixture, forcing heavier contaminants to rim of the centrifuge from which they can be removed. The unsettled mixture is then filtered through a screen that traps unbroken bits of paper and debris. The bits of paper, called flakes, can be washed off and returned to the ragger for further processing.
Stock that makes it through the screens continues to the final stages of the process. The fibers get blasted with high pressure water to clean them. Next, the water is treated to remove any chemicals that were added to remove ink.
Finally, the fibers are filtered through a fine mesh screen into a tank where the water is drained off, called the clean stock chest. This stock is now ready to be made into paper, the same way as fresh stock from wood or cotton.