Make a rough sketch of the outdoor space where you want to build a brick flower bed. Choose a space that is easy to access and maintain and note how much shelter and sunlight the area receives. Pencil in any trees, existing structures or well-established plants that may influence the size of the hexagonal brick flower bed you want to construct. This will help you determine how big you can make the bed.
Mark the ground with spray paint, stakes or string where your tentative flower bed will go, and calculate how many bricks you will need to lay down as the first layer. Take note of the length of your flower bed's sides, as well as the length of your uniform bricks or blocks. At this point, you can adjust the size of your hexagon-shaped flower bed, just keep the sides equidistant to stay true to this shape's geometry.
Prepare the site of your future flower bed by removing the top layer of grass with a shovel and make the ground level if it is not already. The Home Depot Garden Club suggests digging a trench one to two inches deep where the flower bed border will go. It is unnecessary to remove the turf of a raised bed. You may have to remove or trim back any well-established plants that will interfere with the construction of the flower bed or new growth.
Lay down your first layer of bricks along the edges of your hexagonal flower bed. Fit the edges of each side together snugly to create the sharp corners of a hexagon, or have the bricks meet at their corners to create a different six-sided design. Continue adding layers of bricks on until your hexagon-shaped border reaches the height you desire.
Fill your geometric-shaped flower bed with soil and some compost or manure if you desire, until the bed is nearly full to the brim. Fill your raised, hexagonal bed with your favorite flowers by starting them from seeds of planting specimens from a local nursery.