Don't worry about being too gentle, DMC threads and aida cloth can take a lot of wear and tear. I wash all my washable cross stitch (as opposed to the non-washable kind, anything done in a specialty thread like a hand dyed or over dyed thread) in a tub of warm water with Ivory dish soap. Any marks I scrub, doesn't hurt it.
When I've rinsed, I place face down on a towel, roll gently and pop it into the freezer. The next day, I pull it out, let it thaw for a minute or two, gently unroll and press. The steaming action does a wonderful job of taking out any wrinkles, fold lines, etc...and makes it great for cutting and sewing. Plus, the smell of the Ivory soap is an added bonus.