The process of building a conversational AI system involves seven steps: gathering utterances and transcripts, building an intent model, defining the scope, planning happy paths, building out long tail design, QA and launch, and business as usual monitoring. This iterative process requires ongoing effort to continuously improve and refine the agent's performance. The timeline for building an agent can vary depending on factors such as call volume, data availability, and stakeholder feedback. A well-planned approach with clear goals, scope, and timelines is essential to ensure a successful launch and ongoing maintenance of the virtual agent.