When the time comes for me to make more slip, I just take some of the dry paperclay, put them in a smaller bucket and then pour enough hot water to totally cover them. Do not mix at this point. Let it sit overnight if you are not in a hurry. If you are, you'll be amazed how fast the dry paperclay softens up - uusally within the hour. I find hot water or boiling water speeds up the softening process.
After the paperclay has soaked up all the water it can hold (technical term, this is called slaking), I pour out the excess water. You can save this water or discard it. After stirring and thorough mixing, you can decide what consistency of paperclay slip you need. To thin out your paperclay, add back the water you just poured out or add fresh water. To prolong the shelf life of your paperclay, I add a capful of bleach (or any disinfectant) at this point and stir well.
It's best to make fresh paperclay slip as you need it, but as we all know, we tend to get lazy and opt to make a large batch and have it at our disposal.
Old paperclay slip can be dried out and remade into slip using the method described above. It's best not to mix old paperclay slip into freshly made one as you are contaminating the fresh batch with whatever is "growing" (ie mold, etc) in your old batch.