If the stuffed animal is not very dirty then you can use a damp washcloth and some vinegar to help clean the stuffed animal.
I found that when my kids stuffed animals got a bit dirty all I had to do was to get a wash cloth damp with some vinegar and then wipe the stuffed animal down and usually the dirt and anything else would come off of it.
But if the stuffed animal was really dirty then I would place the stuffed animal in the washing machine but the washing machine I used did not have an agitator in it.
I once tried washing my kids stuffed animal in a washing machine that had an agitator and the washing machine ripped the poor stuffed animal bears head off.
My kid was so upset and he was only 3 at the time.
He got mad at me for that but now we look back on it and laugh now that he's nearly 18 years old.
As long as your washing machine is one without the agitator though then you can safely wash the stuffed animal in the washing machine.
Or you could place the stuffed animal on the top rack of the dishwasher to wash it safely which I've done before myself.
Then you can dry the stuffed animal in the dryer as long as it doesn't have any plastic parts such as plastic eyes etc.
Another way to wash stuffed animals is to just wash them in a tub of warm water and then squeeze the water out and let it dry naturally or put it in the dryer to dry.
Just be aware that if you tear the child's stuffed animal apart when washing it then you'll have a mad toddler or child because stuffed animals are their best friends.