Dig a trench into the ground with a shovel that is at least a foot deep to help anchor the wall and prevent collapse.
Fill the trench halfway with broken bricks and stone and then cover that layer with an inch inch of sand.
Pour a layer of concrete into the trench and smooth it out with a trowel. This provides a strong support that restricts the wall's movement once it's built. Cover the trench with a plastic drop cloth while the concrete dries. Once your foundation is set, you can build your brick wall.
Fill the sides of the trench with dirt once the wall has been built. If you have a wall already built without a trench or foundation, add at least 2 feet of dirt or mulch to both sides of the wall to help restrict it from falling.