Excavate the grass and top soil with a shovel where the first column will be built. Dig a hole about 4 inches deep and 10 inches in diameter.
Mix 1 part cement with 3 parts sand in a wheelbarrow, moisten the sand and cement with a garden hose and mix together with a hoe. Add just enough water to make the concrete a pasty consistency; too much will ruin the mix, making it unusable.
Pour the concrete into the hole and lay the first bricks. Fill the gaps between bricks with concrete, using a trowel. Scrape excess concrete away with the trowel blade. Allow the first bricks to set into the concrete for a period of 12 hours before proceeding.
Rinse out the wheelbarrow and set aside until the first layer is dry.
Mix more cement with sand and wet to form another batch of concrete. Spread concrete onto the first layer of bricks, filling the gaps with concrete, using the trowel. Build the column up to the desired height and let it dry for 24 hours before attaching a fence panel or rail.
Repeat the process for each successive brick fence column until finished.