Amigurumi (crochet or knit stuffed toys) including felt need to be washed differently than those without felt because the felt is made of a different material, and needs to be handwashed. You can tell if your piece has felt on it by checking for any flat shapes sewn onto it. In the image to the right, there is felt sewn onto both the cap and the body of the mushroom. (Pattern by Critter Stitch Designs.)
The felt I use is from Daiso. According to their website, it's polyester, so, like the yarn I use for amigurumi, it's synthetic. Similarly, I use Poly-Fil, which is made of polyester too. This means that you should keep your piece away from heat to avoid the plastic melting. Generally speaking, synthetic fibers start to become damaged at about 200 degrees Fahrenheit, so a hot day won't damage your piece, but you should avoid sticking it in the dryer. Instead, use a blow dryer or let it air dry.
Because of the felt and sometimes delicate nature of the stitching on pieces that include felt, I highly recommend handwashing your pieces. You don't have to be picky about your soap, just make sure it's decently mild and that you only use a small amount of it. Literal baby shampoo will work. Wash your piece in cold or lukewarm water, and do not rub aggressively at the surface, as this can damage the material. Generally speaking, be super gentle when washing amigurumi. You can usually get away with using just water to dab away at dirt unless your piece is super dirty.
If some yarn comes loose, you can use a tapestry needle to weave it back in again.
Unless otherwise requested, amigurumi I make uses plastic safety eyes. Keep these away from small children and pets, because they can snap off easily and become a choking hazard.