Initiating a mobile number portability request to switch away from MTNL to another telecommunications operator involves generating a Unique Porting Code by sending an SMS with the keyword "PORT" followed by the ten-digit mobile number to 1900. The subscriber must clear all pending outstanding dues on their postpaid account or ensure a valid active status on prepaid numbers, obtain the porting code authorization, and submit a formal switching application along with valid identity verification documents to the new service provider.