With my cross stitch projects, I do wash them. I get a glass brownie/casserole type of pan
( like pictured in this image - not my image! http://iweb.cooking.com/images/products/enlarge/159018e.jpg
fill it with warm water and just a little bit of mild dish soap. I then submerge and swish around my project to get it nice and wet, but not super sudsy or anything. then I rinse with cold water gently. Fold it up in a towel, pat it to get some water out and then take out my iron to iron it gently to get all the crinkles out from the hoop and dry it the rest of the way. I find that a lot of grease from my hands being on it comes off and once its ironed, its super nice to present to someone or frame etc. And it smells nice! haha. I do not throw it in the washer or anything like that. I don't know how that would turn out.
This is basically what I do. I've only been cross-stitching for a few months but my mother has been for 25+ years and this is what she taught me. I roll mine in a thicker cotton dish towel to absorb most of the water then iron between the folds of a thinner cotton towel (such as the single layered ones that are often embroidered).