LmouthBass has the most in-depth description I have ever seen for setting up a 10-gallon pet aquarium. If you ever want to get into the hobby seriously, I think he's a great person to talk to.
All the testing supplies and constant water checks are not necessary if you want your kids to maintain any type of interest. Here's my two cents
1. Make sure you have a thermometer (stick on is fine), a heater and a small bottle of water conditioner. The instructions for use on the heater are easy to understand.
2. Rinse the gravel before you put it in the tank! Put the gravel in the tank and fill with water. Put in the water conditioner. Place plants in a beautiful arrangement (this is great for the kids). Place the filter and heater on the side.
--You can put as many decorations as you want in the tank, but keep in mind, the focus is the fish. I would say 4 or 5 plants (if you're going synthetic) and a nice castle or driftwood. Fish do need hiding places to act normally.
--I do NOT recommend real plants. They require a little more attention and although they are beautiful, if things go wrong, the tank quickly gets very unsightly.
3. Let the filter run overnight. Go to the store the next day and buy ONE or TWO hearty fish (mollies, platys, a betta, guppies). Leave these two (or one) fish in the tank for about a week or two. After that, add fish slowly, up to three at a time, with the same amount of time between.
THAT'S IT. If you want to set up a tank without spending $150 bucks on testing equipment and water additives, add 2 hearty fish, wait about 2 weeks and I promise you it will be cycled.
This is a fun and interesting hobby. If your kids are going to be the caretakers, get the MOST hearty fish you can (the ones I mentioned are EXCELLENT).
One final note. The general rule for fish is 1 inch of fish per gallon. The fish I mentioned will grow to about 1.5 in. Therefore you could keep about 6-8 fish in a well-run 10 gallon tank.