There's a very good book, 'Absent Friend', by Laura & Martyn Lee, ISBN 1850540896 and still available from Amazon. It deals with all aspects of the death of a pet, including coping with your feelings, helping the children, dealing with the practical side of things and, importantly, what happens physically when an animal dies. For instance, dogs don't close their eyes in death, which can be upsetting to some people.
I bought after the death of a much loved Bassett Hound, and I really wish I'd read it before that, as I would have been much better prepared for the loss.
I think it's important to be honest with your children and don't conceal things from them. Let them be as involved as they can/want to be according to their age. I remember as five year old being told that our dog had gone to sleep at the vets and would be better when he woke up. He'd had to be put down because he had distemper, and I resented my mother for a long time after I was old enough to know the reality.