In the simplest terms, permaculture-style berms and swales can be defined as a ditch, on contour. The swale is the ditch. It is designed to hold water, sinking it down into the landscape and temporarily raising the water table. The berm is a small hill, constructed on the downhill side of the swale, which increases the amount of water that can be retained.
Looking at the profile view of a berm and swale, they form a shape something like an "S" with the swale dug out from the hillside to create a downward arc, and the berm built up above the hillside to create an upward arc. In many permaculture design plans, berms and swales are represnted this way in the plan drawing, wtih a sideways "S".
Berms and swales are always built on contour. This means that they are built on a level cutting through the surrounding terrain, sometimes across great distances, so as to retain water evenly across the length of the swale. Because they are built on contour across the landscape, berms and swales can sometimes resemble elevation lines as you would see on a topographic map.
Building berms and swales is never as simple as just digging a ditch. Keep in mind that these ditches are planned using the principles of permaculture design, so it is likely that many months of observation, microclimate conisderation, and the needs of countless stakeholder species have been taken into account in designing these particular ditches.
In addition to the needs of the stakeholders, the needs of the land itself are taken into consideration in choosing the physical location of each berm and swale. Some people take a more organic approach to this part of the design process, crafting small berms and swales that feed into one another at strategically-chosen points as water descends a hill. Others rely on advanced math to choose the ideal spacing and location of each set of berms and swales.
You can see a great example of these two approaches in Paul Wheaton's World Domination Gardening videos. The initial design plan for the site that is developed in those videos uses long, even berms and swales that run the length of the design site. Paul's on-the-fly design edit breaks up those long lines into smaller swales that feed eachother to evenly distribute the flow of water and avoid large channels of rainwater run-off.
Only after all of these planning factors have been considered is ground first broken.
The first step in building berms and swales is to find and mark a level line across the contour of the land. There are different methods to accomplish this - some are cheap, and others are fast. If you don't already own your own equipment, you'll have to choose between cheap and fast - one or the other.
The fast way to mark a level line across the contour of a landscape is by using a laser level that projects a level line across the terrain. Using a laser level, the operator can simply walk across the land and mark the laser's line with stakes or paint.
The cheap way to mark a level line across the countour of a landscape is by using a bunyip, or water level. You can create your own bunyip using nothing more than some clear tubing, duct tape, and a few yardsticks. Using a bunyip, you use water as a tool to create a level that works over distances of 10 or 20 feet. Each time a level is established, a marker is set, and one end of the bunyip is moved to the next location.
After level lines have been drawn to mark the spot for each set of berms and swales, digging commences. For large-scale projects, machinery is often used to dig out a swale quickly and then pile the excavated soil into a berm on the downhill side.
Some people prefer to use shovels and picks rather than heavy machinery - sometimes becuase some factor prohibits access for machinery, and sometimes becuase the designer's preference is to avoid the compaction of soil that can be caused by heavy machinery. When berms and swales are dug by hand, the swale is dug first. The excavated soil is placed directly behind the swale on the downhill side, to create the berm.
Berms and swales are an excellent strategy for forest gardening. They are capable of sinking water deep into the ground where it becomes available to the roots of trees and shrubs. Berms and swales are not a great idea for most annual vegetable gardens, which can be fouled by having too much water present in the soil for too long a time.
A common practice is to intensively plant along the top of the berm. The soil top of the berm is thoroughly watereted each time enough rain falls to fill the swale, but this area is relatively well-drained because of its elevated height. Intensively planting the berms increases the sturdiness of the design overall by securing the newly-disturbed soil with an abundance of plant roots.
Berms and swales have played a pivotal role in many famous permaculture installations, including Geoff Lawton's Greening the Desert site in Jordan.