My children regularly had wash days for their dolls when they were smaller. We would set up wash tubs or big bowls with a bit of soapy water and some clear rinse water. They would string lines between trees decorated with their own colorful clothes pins. Then, they would gather all the doll clothes for washing. They were incredibly industrious in this wet endeavor.
Once the clothes were dry, newly freshened, the accumulated smudges and scuffs and stains on their dolls would become more obvious. The contrast between the clean clothes and the scruffy dolls was too great, so a dolls' bath day seemed a necessity. And this, the bathing of the doll, can feel as important as bathing a tiny baby. Your child will probably be intrigued by the water and soap and gentle care even if their thoughts don't always run to dolls.
If your child has a Waldorf doll with wool stuffing, you have probably wondered just how much washing the doll can take. Really, a sponge bath with a little soap, a soft rag, and a little warm water is the best for the doll and often get them clean enough. In this scenario, your child handles the doll like a newborn, not yet ready to be submerged in water. Explaining to your child that this is how you washed them when they were a baby can be a nice way to connect the doll and your child. Start with you or your child undressing the doll. Take a soft wash cloth, like the less abrasive ones you might have used on your children or a bit of flannel, and dip it in warm soapy water. You can wash/wipe any surface dirt, trying to rub gently as the cotton fabric of the skin can get nubby with too much rubbing. Then rinse the spot with a cloth that has been dipped in clear water. Let the doll air dry, which should not take long if you have only done a surface washing.
Sometimes, a doll needs a complete tub bath, and wool dolls will survive a gentle one amazingly well if care is given to keeping the stuffing in the right form. The sink or a smaller plastic tub make good doll bathtubs because the amount of water is limited and you can arrange a work surface for the first round of drying. Again, you will want some gentle soap, a soft cloth and pleasantly warm water. You will also want an absorbent bath towel. Simply set the doll into the warm (not too hot, not too cold) water and bathe it, remembering to go easy on the scrubbing. A little soak can help with any stubborn dirt. You or your child should be extra gentle when cleaning the doll because the filling can more easily be misshapened once the doll is saturated.
When the doll is as clean as it can be, let out the water and lay the towel out. Set the very wet doll on one end of the towel and roll it up. You want to squeeze, but NEVER wring, some of the water out of the doll with an eye toward keeping everything the right shape. Then unroll the doll from the very wet towel. After this, find a warm, safe place to lay the doll flat so it can dry. Direct sun is not recommended. It can take a day or more for a doll to dry completely, but once it is dry and fresh as a daisy, your child can dress it and get back to their play.