(Ed’s intro: Keep in mind that there are two primary concerns with a getting a cloth wet:
1) Wetting the cloth may be considered to be laundering it, especially if it is soiled, and 2) Wringing out the cloth is always forbidden. I will try to provide a heading for each paragraph in order to aid the reader – and the writer!)
32) Cleaning a garment, drying hands on a towel. A garment that is soiled may be wiped with a rag or the like [Footnote #121: It may be wiped lightly, so as not to squeeze the dirt (oil etc.) out of the garment], but water may not be spilled on it, because spilling water on a soiled garment is equivalent to laundering. Therefore, if a child urinates on a garment, it is forbidden to pour water on it. (Note: If the child urinates on the ground or on a wooden vessel or animal hide, it is permitted to pour water on those, as these are not made of cloth.) When one washes his hands and wants to dry them with a white towel, he should first rub his hands together well to remove the excess water, so that only a little water remains on them. With a large amount of water on the hands, however, drying them on the towel is seen by some authorities to be akin to laundering it! (Footnote 124: This is a proper custom, but according to halacha, it is permitted to dry your hands – on a white towel - even with all the water on them and even if the towel is soiled! Ed: A colored towel does not present a halachic problem in this regard, according to all opinions.)
33) Covering a barrel with a cloth. A barrel containing water or other liquids may not be covered with a cloth which is not set aside to for this purpose, lest it become wet and be wrung out. If the cloth is set aside for this purpose, it may be used to cover the barrel, for then we have no reason to fear that it will be wrung.
34) Wiping up a spill, drying dishes. If water spilled on a table or other surface, it is forbidden to wipe the spill with a clean garment of value, for since it absorbs much water, you may inadvertently wring it out. (Footnote #125: If the garment is dirty, even if it has little value, it may not be used, because then, getting the garment wet in the first place is like laundering!) Similarly, using a towel to dry cups or other vessels that have narrow openings may be forbidden as well, because ten liquid is more easily squeezed out of the towel. (Footnote #126: If water spills on a tablecloth, wiping it up has the additional concern of spreading the water to soiled areas of the tablecloth.)