An ice cream recipe simple enough for kids to make calls for 1 quart of heavy cream, 3/4 cup of sugar, a pinch of salt and 2 teaspoons vanilla extract. Mix the ingredients, place in an ice cream maker and follow the manufacturer's instructions.
The simple recipe above, from FriendsandFarms.com, also includes some variations to make other ice cream flavors such as strawberry, peach and coffee ice creams. Just substitute the vanilla extract with other extract flavors such as almond, butter, rum, orange or a combination of different extracts.
There is also a way to make ice cream for kids without an ice cream maker at home. The How Stuff Works website has instructions on making ice cream at home with pint-sized and gallon-sized zip top bags. The recipe for this method calls for the same basic ice cream ingredients as the recipe above, but only enough to make a pint of ice cream. Gather 1/2 gallon ice cubes and 6 tablespoons salt for the project.
Put the salt and ice in the gallon bag and mix, then place the ice cream ingredients into the pint-sized bag and seal it tightly. Put the pint-sized bag inside the gallon-sized bag, seal the gallon bag and surround the ice cream mixture with the ice and salt mixture. Wrap the bag with a cloth or use insulated gloves, then shake the bags to keep the cream mixture moving while it freezes. This prevents ice crystals from forming.