To apply for passport services through the Passport Seva Portal, users must first register by creating a user ID and password. They can then login and select the required service, choosing to either download and fill out an offline application form or fill out the form online. Users must then schedule an appointment at their local Passport Seva Kendra (PSK), selecting an available date if paying online is required for their PSK or simply booking after paying. They should print their application receipt with their appointment details.