The idea of terracing is to make the hillside into giant flat steps that will allow for planting beds and keep soil from washing away.
You can make terraces into interesting shapes, curve them around a seating area, divide them up with a staircase down the middle or use them in many other decorative ways. You can even use less visible step areas for cutting gardens or vegetable gardens.
To terrace a hillside, you will want to cut very wide step-like areas out. Usually this is done starting at the base. Flatten out the top of a raised area, butting the front against some form of retaining wall. When the soil starts to pile up behind the flat area, build another retaining wall and start flattening out the second tier. This will continue up to the top.
The barrier to keep soil from tumbling forward in the front of each 'step' needs to be solid and firm enough to keep the soil behind it in place. A retaining wall can be built of rocks, bricks, cemented blocks, interlocking blocks, railroad ties or many other materials. The more weight behind it, the more solid the structure should be.
I recommend adding a drainage pipe and gravel -- or at least a buffer zone 10" deep of gravel behind the back of each retaining wall. This will keep water from backing up against the retaining wall.
Terracing slopes can be a practical and decorative landscaping solution to keep a hillside erosion free.