Preparing for a customer support interview at Intercom requires understanding the company's values and the interviewing process. The process involves multiple stages, including an application and phone screen, a take-home test, a manager phone screen, and a virtual onsite interview. To make a great impression, it's essential to practice storytelling, use the STAR framework, ask questions at the end of the conversation, and be prepared with technical skills for Support Engineer roles. Intercom values seven key qualities: being an owner, connecting personally with empathy, thriving under pressure, giving feedback fearlessly, focusing on fundamentals, being resourceful, and practicing patience. By understanding these values and preparing accordingly, candidates can increase their chances of success in the interview process.