Actually, the process can be VERY different.
Kraft digestion and Sulfite processes are primarily chemical and heat-based. Then there are thermomechanical process that are used to make groundwood pulp for newsprint, etc. Depending on the qualities needed in the final product, mills often bleach the pulp with chlorine, chlorine dioxide, peroxide, or other oxygen processes.
To make recycled paper, you need a suitable source of paper, and you need to balance the availability of those sources against the value of your finished product, and the costs of making the used paper usable. You have to consider the costs of maceration, de-inking, removal of higher AND lower-mass contaminants (requiring two different types of centrifugal cleaners), etc, etc. And again, if you need white pulp, there has to be at least a simple bleaching stage.
Any one of these processes could be the subject of a lifetime's study and work, and can't be described in an on-line forum comprehensively, or with reasonable accuracy. Use Google, Wiki, and other on-line tools to steer you in the right direction. You'll be at it for a while, guaranteed.