Canteens or plastic bottles filled with water are vital for any hike, no matter how short the trail. You'll need to have enough of them to carry about 2 pints of water per person for every hour of hiking. If going into arid regions, you'll probably need more.
When looking for a canteen or a water bottle, make sure it seals tight and can be stored upright in a carrying case. The carrying case should hook to your backpack or fanny pack belt. You don't want to place canteens or water bottles loose in your backpack, or they could drip, leaving your gear and extra clothing wet.
Another possibility - and one popular with kids - is a hydration system. A lightweight plastic bag connected to a plastic tube can be filled with water and placed inside a daypack or a fanny pack (some backpacks come with them built in). The child then can drink water as walking simply by sucking on a tube, as if an astronaut in a space capsule. Since it's so effortless to use, kids tend to stay hydrated with it. Some hydration systems will hold up to 35 ounces of water, which is little more than a quart.
Read more about day hiking with children in my guidebook Hikes with Tykes.