AXIS, Kotak, HDFC and ICICI have the pre-written template form that you just need to fill out on their customer desk. You just need your identity proof and the signature on that form. You don't need to write any application in regards to the new ATM or lost pin or change of address, phone etc. In order to request this information you can also use Kiosk or the netbanking as well.
If your bank is SBI, IDBI or any other semi or govt funded bank then in that case you need to write the letter to the bank manager. You have to mention the following way.
I have lost my existing ATM card (or insert your reason for requirement of new ATM). My account ID ____ and my identity proof and PAN attached.
This is the application that you can post in respective banks. And they should process your ATM card application.