When I wash placemats, whether they're "store bought" or made by me, I wash them on the "hand wash" cycle on my LG washer and then since they come out nicely damp (not wet), I lay them on layers of old bath towels. Do not machine dry them. I put the placemat down, cover with 2 thicknesses of towel and repeat. I often just spot clean if the stains aren't really grotesque! As I make the layers, I smooth each one with my hands. I never have any problems after that!
Be careful how you wash the mats. If you want to machine wash them, do it on the most gentle cycle as possible. Alternatively, hand wash them if you want to. I just bought the Oxy Clean gel stick to pretreat. I got it at Target and if you go to the Oxy Clean web site, ther's a 75cent coupon.
Missy B