A ritual can be as simple as lighting a candle, reading out a poem or saying a prayer. It can be cremation or burial in a pet cemetery, service in the back yard or a walk in the park.
Rituals should be encouraged to allow the grieving people to say their goodbyes. Some people make scrap books, put up photos, post photos on web sites. You could sponsor a cage at an animal shelter giving it the name of your animal.
Do what makes you or the child feel comfortable, let the child have a say in the ceremony, and if they’re not comfortable don’t force it, you can say goodbye in your own way. Writing a poem, drawing a picture or writing down memories can often help.