Regardless of the angles of curves in your brick edging, you need to follow the same basic procedure for laying bricks in a way that will last. This involves placing stakes in the ground and running a string between them to indicate the shape of your edging and all of its angles. Dig a trench that is several inches shallower than the thickness of the bricks you plan to install following the line of the string. Tamp down the soil that forms the base of the trench to create a firm foundation for the bricks.
The easiest brick edging angle to install is a 90-degree angle. Since the bricks are already rectangular, you can create this type of angle without any cutting or special planning. Instead, finish the first course, or line, of bricks before laying a brick that abuts the first course's final brick and begins a new course of edging in a perpendicular direction. Check the angle using a framing square to ensure that it measures 90 degrees.
Brick edging angles other than 90 degrees are more difficult to plan and install. To create another angle, use a masonry saw or brick chisel to cut one or more bricks to form the desired angle. An acute angle (less than 90 degrees) requires you to cut off a corner of a brick on the second course you install. An obtuse angle (greater than 90 degrees) will create a gap between the bricks closest to the corner, which you can fill with a small wedge-shaped piece cut from another brick.
As you lay brick edging, add soil to hold each brick in place. This ensure that your courses are straight and your angles are even. For each brick, use a mallet or piece of wood and hammer to tamp it into place before moving on. If you don't like the look of sharp angles, consider laying brick edging that follows a sweeping curve pattern. To install this type of edging, simply angle each brick slightly to follow lines that you mark with chalk before cutting the trench.