If you grind wet it's a mess, also you have to get everything cleaned up before it has a chance to dry. If you do it wet, I would do a small area and then clean it well before going to the next section. If you do it dry it makes a bigger mess but it's all concrete dust and can be vacuumed up.
When I did mine, I rigged up an Dust Deputy setup http://www.oneida-air.com/category.asp?Id={CC6B6F2A-E3D7-4F18-A53C-B5C357DFE131} to my shop vac for cleaning the floor. After getting up as much as possible, with that setup, I then pressure washed it 3 times, before I couldn't get anything on my hand, when I rubbed it across the floor.