The cost and type of arrangements depends on your veterinarian, where they put their client's pets to rest, and what they charge (anywhere from $100 and up) This would include cremation. Burial in a pet cemetary and/or if you choose to have your pet placed in an urn, can be similar to that for people. The other option is to have your pet cremated and placed in a mass grave at a pet cemetery.
As for you and your children, losing a pet is just as trying emotionally as losing a human family member. From here on out, begin preparing your children for the loss by reminding them to spend as much time as possible your dog. Tell them that she her time is short, but she'd really appreciate and love her family around her more than ever, and would probably enjoy extra brushings, extra pillows, extra hugs, etc.
Encourage them to take lots of pictures, and maybe even assemble a collage or scrapbook so that when your dog is gone, they will have happy memories and pleasant pictures to look at.
You may want to think about whether or not you want your children to go with you to the vet when and if you have to put your dog to sleep. You know their temperments. If they're extra sensitive, it may not be a good idea...though the vet will not let you see the actual procedure. They usually let the family say their final farewells, and then escort the family from the room.
In case your pet should die at home, keep a quilt handy, and wrap your pet in it. Sometimes, there is a bit of a mess after death, so be prepared for cleanup. Once again, you may not want your children to see this, so have a plan in place. Call you vet to let them know, and they'll more than likely have you bring the pet to them, or wherever they do cremations.
Just like with a human funeral, you may or may not want to plan ahead by picking out urn, whether or not you will purchase a burial site, and what you as a family may do to memorialize your pet.
This is very difficult. But planning ahead may help some. I have lost two dogs over the years, and I still miss them so much. I currently have a very old Lab who I expect doesn't have much time. Don't expect to get over it soon. Just like a loss of a close relative, it's good to tell stories and remember the good times..maybe even some of the bad ones which can be funny in retropect.
Last but not least, if your pet hasn't passed yet, don't act glum around them. They are very intuitive like people and your dog may get frightened or even depressed. Now is the time to treat your dog like the royalty they are, and enjoy them and make their last moments at home wonderful.