There are many ways to approach design.
However, most of the time they will involve these steps in this order: gathering information, objective development, design generation, and production. These steps are not exhaustive. And I've left many issues out, because everything depends on the project and expected outcome. That's one reason most designers produce different price quotes for different projects, even when the final outcomes may be similar. For instance, let's say two different companies want a website. The projects seem the same, but one may require logo design, photography, and custom e-commerce solutions. Features like these affect the work and time involved, and are hard to predict unless appropriate information is gathered first. Here are my steps in general:
Gathering Information.What does the client want to achieve? To promote something, to inform, to establish, to create a specific thing, etc.? At this point, listening to the client is most important. The purpose is to gain an understanding of the client, the environment they occupy, their audience, and their messaging and brand. And come away with a few key objectives that would make the design project successful.
Objective DevelopmentSometimes it is necessary to gather more information beyond what the client supplies. But in either case, good designers have to synthesize the information into a structured plan. Unless the client supplies a detail project brief, the designer usually would supply a creative brief to ensure that both the client and designer are in agreement in a design approach. Sometimes at this stage the designer may even provide sketches or wireframes for web design.
Design GenerationAt this point there is a clear agreement in the approach the designer and client would like to engage. And the designer begins creating visual design concepts. In some cases, the designer may produce two to three options for the client to choose, or provide one clear direction of the designer's choice. (This depends on the level the trust a client wants to give a designer.)
ProductionAfter a design direction is chosen and everything is approved by the client, the design concept is fully realized and implemented. This may mean anything from printing and distribution of a brochure to the testing and public launch of a website.