A design approach is a general philosophy that may or may not include a guide for specific methods. Some are to guide the overall goal of the design. Other approaches are to guide the tendencies of the designer. A combination of approaches may be used if they don't conflict.
Some popular approaches include:
KISS principle, (Keep it Simple Stupid, etc.), which strives to eliminate unnecessary complications.
There is more than one way to do it (TIMTOWTDI), a philosophy to allow multiple methods of doing the same thing.
Use-centered design, which focuses on the goals and tasks associated with the use of the artifact, rather than focusing on the end user.
User-centered design, which focuses on the needs, wants, and limitations of the end user of the designed artifact.