To apply for passport services, users must first visit the Passport Seva Portal and register by creating a user ID and confirming their email. Once logged in, applicants can select the required service and choose to either download an e-form to fill out offline and later upload, or fill out the application form online directly on the portal. After submitting the application, applicants must schedule an appointment at a nearby Passport Seva Kendra (PSK), pay the application fee online, and print the receipt with their appointment details.