When I create signs in my basement shop, I don't have a sink to rinse off my Ikonart stencils right away. To get around this, I put the clear backer sheet back on my stencil immediately and stick it in a tote with a little bit of water. At the end of the day, I take the tote upstairs and rinse out all the stencils. (If I'm being real, in a perfect world I do this every night, but there have been occasions that I have forgotten and rinsed them out the next day - it has never been an issue.)
First, use warm water to remove any excess ink or paint from the stencil. Usually, this is enough to ensure the stencil mesh is clean. Don't worry about removing all the paint from the front of the stencils - often the paint will stain the stencil material. As long as the mesh part of the stencil, where the design is, is completely clear, you're good to go! You can hold the stencil up to a window to make sure all the paint has come out and you can see through your design.
If you have stubborn paint that won't come out, you can use a mild dish soap like Dawn PowerWash spray. Mix a small amount of dish soap with warm water and apply it to the top of the stencil. Rub lightly with your fingers to remove the paint from the mesh areas. Repeat this process if needed.
Make sure to rinse the stencil thoroughly with warm water to remove any remaining paint and/or dish soap.
Once rinsed, lay the stencils on a flat surface to dry. Keep the clear backer sheet on or the stencil will stick to the surface and be ruined. Gently pat the stencil dry with a paper towel and let it air dry.
Proper cleaning and care of your stencils will help ensure they last for multiple uses!
If you prefer to see things on video, here is a video for you showing my process:
