To register for the IPU CET exam, applicants need to provide personal details, academic records, exam preferences, and upload required documents including a photo, signature, and thumb impression. The registration process involves creating an account on the IPU website, filling out the online application form, uploading documents, and paying the 1000 INR fee via online payment. Applicants can check the status of their application and make corrections within 5 days of the last registration date by submitting the form physically with a 500 INR fee.