Sorry about your dog What's the timeframe for the decision? I'd start talking to them about how the dog is old and poorly, and the vet can't make her better. Avoid the phrase "put to sleep" as it can make some children fearful of sleeping or of anaesthetics. I wouldn't have them there when the dog is euthanased if you can avoid it. Having a funeral can be helpful, either burial, or cremation with return of ashes to scatter or bury, or bury collar, photo, pictures etc. Expect lots of questions for some time after, small children need to 'rehearse' what happened to process it - tough on you if you are grieving for an old friend.
Just been through this with my 3 1/2 year old and 2 1/2 year old. I avoided the whole put to sleep phrasing and I think I told them that the dog was very old, ill and that it was an ill the vet couldn't make better and so the vet was going to give her an injection so it wouldn't hurt her anymore but that she would die and wouldn't be coming home.
This bit is obviously dependent upon your beliefs but I told them that I liked to think she had gone to be a star in the sky watching us and thinking she'd love to steal that sandwich we were eating (dog was a fantastic thief) which dd1 thought was hilarious.
There's an episode of Topsy and Tim that covered it recently too which appeared about the same time we lost our dog