How do you get your puma tennis shoes clean?

OK, I have some hot pink and orange pumas that I love. I use them for volleyball. They have gotten pretty dirty I do not want to put them through the wash they have like white net stuff on the front. if you google Puma Women's Cell Volt Running Shoe Silver/Orange/Pink (you can highlight it then ctrl+c then then ctrl + v) it is the first pink and orange and silver tennis shoes you see so you know what i am working with. please tell me what i can do for them thanks so much