Most of the banks have their applications called app in general. You can get online netbanking services without visiting your bank branch office. Here are a few points to make it clear:-
1. You should be the single user for your bank account ( no other joint holders) to avail this facility.
2. You should have an ATM card which is used and not stagnant over a period of time.
3. Your mobile number should be registered in your branch to get one time password.
4. Keep your bank passbook and other documents like ATM card, CIF number ready with you for immediate access.
Check whether your bank has an app and download it. Complete the required fields for new user registration like registered mobile number, CIF number and wait to get an OTP. This will help you to create your password to login. Check step by step user friendly questions and answer correctly. Once this procedure is cleared, you could check your balances, debits and credits. This will help you to use internet banking facility. If any doubts and mis-clarifications, you may have to visit the branch itself.
You can also refer to this link onsample letter format to get internet banking facility
write a letter and use postal services or email facility to send your letter to the branch office.
These are only the few steps to be followed, it may differ from bank to bank. Money matters have to be dealt carefully. It is better, to speak to your bank branch manager and take necessary actions accordingly.