The engineering design process involves defining an environmental problem, researching potential issues, brainstorming solutions, choosing one topic to focus on, building a plan to address the chosen topic, testing the plan with feedback, communicating the plan to others, and redesigning based on received feedback. This team defined air pollution from vehicles as their problem, researched the issue, developed a plan presented on their website and display, received feedback from teachers, and then redesign their project based on that advice.