How does water carve rock? How does water carve rock?
And more generally, how does a soft material carve a hard material?
Obviously it happens, but is it a continual process (every drop of soft water carries away a minute amount of hard material) or is it a stochastic thing (every once in awhile, the force of the water just happens to exceed what's necessary to snap off a grain of sand)? Or is it something else (the erosion is actually caused by hard pieces of grit carried in the water)? 
UPDATE: Grit certainly plays a major role in actual weathering, but is it necessary? Would pure water ever erode rock?
 A: There are lots of different types of rock, and water can vary in it's acidity, so there are a few variables to consider.
One obvious example is the formation of caves. These are usually in limestone, which is calcium carbonate. If carbon dioxide is present, calcium carbonate will dissolve in water to form calcium bicarbonate. So pure water (OK with a bit of CO2 :-) will happily dissolve limestone.
Another example is in forming gorges like the Grand Canyon. If the surrounding rock is limestone then the gorge forms by dissolution just like a cave; in fact many gorges are actually collapsed caves i.e. a cave forms first then the roof collapses. In the case of the Grand Canyon the rock contains some limestone layers but there is also a lot of sandstone. Sandstone is silica (silica grains loosely bonded) so it isn't soluble in water and wouldn't be eroded just by solution. In this case the erosion is mostly by abrasion of rocks carried in the water, though any limestone present will dissolve and undercut sandstone layers above it. Sandstone is quite soft and easily abraded. If the rock is granite this is very insoluble and very hard so it erodes only very slowly. I'd guess the main water based ersion method would be freeze thaw cracking.
You expanded your title to ask about any erosion of a hard material by a soft material, but rock ersion by water is not a bad place to start as it's quite varied.
Martin Beckett mentioned water jets, and this is another good example if a bit specialised. If you fire the jet of water fast enough it's momentum means it will break off bits from a hard material. I can't think of any example where this is important in nature.
A: Well I think you have it correct in all aspects, grit would play the major role as would any materials in the water itself.  But while water is still a liquid it contains some sort of friction, more so than air would.  Think of it this way.  Water flowing over a rock after time would smooth the rock much like wind flowing over a desert.  I would say the friction of the water would have to contribute just as much as grima and dirt, grim and dirt simply would make the viscosity of the water greater thus increasing its coefficient of friction.
Hope this helps your thinking
A: Even without the abrasive water is a very good way of cutting intricate metal parts
http://waterjets.org/index.php?option=com_content&task=category&sectionid=4&id=46&Itemid=53
A: At the least, regard it at a molecular level. Molecules in the water cause some molecules on the rock surface to gain sufficient energy to escape.
As a weak analog, think a puddle of water in room temperature. The water will evaporate (water molecules gaining sufficient energy to enter the gaseous state), and that process is assisted by "air" molecules.
A: It is by simply erosion. The higher the water velocity impacts the surface, the faster the erosion or, if by drips, the longer time span it will require. High pressure water jets will erode rock very quickly while drips of water can take eons. But the process is the same. By erosion.
