Measure the length of the bed so that you know how many bricks you'll need. To do this, measure the perimeter of the flower bed and divide that by the length of the bricks to get the number of bricks that you will need to encircle the bed.
Dig a trench along the edge of the bed using an edging shovel. Start at the edge of the grass and drive the shovel straight into the ground, creating a score line all the way around the bed. Move into the bed away from the edge you just cut until you are about an inch wider than the width of a brick that is on end, and cut another score line around the perimeter of the bed. Dig up the soil between the two score lines with the shovel, going deep enough that half of the brick will be buried when placed on its long side in the trench. Make sure that the walls and bottom of the trench are flat.
Compress the soil in the trench with a 2-by-4. You want the soil at the bottom of the trench compacted firmly, making it flat and resistant to pressure.
Drive stakes into the ground at the ends of the bed and run a mason's line between the stakes.
Place a brick into the front of the trench and lower the mason's line until it rests on the top of the brick. Check to make sure that the line is level.
Fill the trench with bricks, making sure that they are level with the first brick. Tap them into the ground with a rubber mallet if they are too high. If they are too low, add more soil beneath the brick. When you reach a corner, run another mason's line along the new edge at a 90-degree angle to the first mason's line. Set the first few bricks on the new side, then use a framing square to ensure that the angle is square.
Fill curved corners with curved bricks, or cut standard bricks to fit in the corners with a wet saw. To cut bricks yourself, lay the bricks over the trench and mark the outline of the curve. Cut the bricks with the wet saw, following the marks you made on the bricks.
Backfill both sides of the bricks with dirt.
Water the area and tamp the soil down with a tamper after you have finished laying the bricks. Using a gentle tapping motion, tamp down on the soil on both sides of the bricks until the soil is flat and compact. This will help keep the bricks aligned straight.