The procedure is quite simple to fill the form as the details of the Rights issue will be already mentioned in the form. The form includes the Rights Issue ratio and the Book closure date.

Fill the mandatory information on the form:
Cheque/DD details (non ASBA)
Select NSDL - if your DP starts with IN (Depository Participant).
Select CDSL if the DP ID is completely numeric.
Your PAN number.
DP details- You can find your DP ID and the Beneficiary number under the profile section.
Your signature or signature of both account holders.
Submit at any branch of a Self Certified Syndicate Banks (SCSBs). Check the series of banks can be found on the application form

Once you complete the issue allotment, stock will be credited to your DEMAT account. This takes a time span of 15 to 20 days from the Book Closure date.

I am enclosing a link of SEBI website. Here you need to submit the online form;