The process involves two steps of iterative collaboration between two ChatGPT-4 instances to develop software from a natural language prompt in Noteable.io. First, one instance will create an initial solution, then the second instance will critique and improve it. This process repeats until a satisfactory solution is found. Key steps include setting up the instances, receiving the prompt, having the first create an initial solution, and the second provide feedback in an iterative process until the code is complete.