Remove the laces and wash them, you can do it in the washing machine with the rest of your clothes.
With a hairbrush carefully scrub the shoes, you can use some water and mild detergent but only on the technical materials, never on the leather.
Let them dry (for at least 24 hours) and remove excess moisture with toilet paper, kitchen towel or a towel. Air dry them, do not tumble dry as this may damage them.
To prevent the slippers from warping or shrinking, make paper balls and stuff them inside the slippers to keep their shape.
The soles can be cleaned with a cloth, wet wipe or brush, keep the transparent sole clean so that the image of your shoe continues to show through.