Its really important to try to find a space to make art. For many years, I worked on my dining room table, and cleaned everything up and put it away before meals. It wasn't ideal for me, as I wanted to make art all the time. So we decided to find space in our home that would be just for making art, and the laundry room seems like a great place to take over, as it has a sink.
The act of working with clay is different than other forms of art. I recommend a dedicated workspace, or a convertible workstation. It could be in the garage, covered patio, or a spare room. If working over carpet, put down some newspaper or a tarp that you can shake outside.
Why all the precautions? Clay is sticky when wet, can clog sinks, and dries to a powder. Students should clean up after using clay with a wet paper towel. If any clay drops to the floor, pick up scraps, then wipe up with a wet paper towel. Do not sweep or vacuum.
At home, I work on top of my washer and dryer. I have a countertop over them that is easy to wipe clean, and the floor is linoleum. I like to work standing up, so it is perfect for me.
As students clean up, have them use wet paper towels that can be thrown away. If they use a sponge or rag and then rinse it out, the clay particles will go down your sink and may cause or add to a blockage. When they wash their hands and tools, have them wipe them off first with a paper towel. I use about 3 paper towels each time I work with clay at home.
When you are done working with clay, make sure you seal it up tightly. I tend to either wrap my piece in a plastic produce bag, or place it in a plastic produce container, with the lid on tightly! Sometimes I do both if I am leaving work for a long time.