India has a form of Dual Citizenship called OCI (Overseas Citizenship of India). If you were an Indian or of Indian origin, you can apply for OCI once you get your US citizenship. There are a lot of advantages to having OCI. With it, you do not need a visa to travel to India. You have the same rights as NRIs, except for voting rights.
Go to your jurisdiction's Indian Consulate website. There should be a link to OCI Scheme.
If you are applying for only one applicant, select 'individual'. If you are applying for your family (up to 4 applicants only), select 'family group'. As soon as you select the family option, you will see 4 application forms.
Verify your information and click submit. A print dialog box opens.
Print a hard copy of Part A and a blank copy of Part B. Only one copy of Part B has to be filled out per family. Both the parents have to sign Part B. In Part A, if a minor child cannot sign in the box next to photograph, place a thumb impression (left for male, right for female) in blue/navy blue ink.
Attach additional documents in the following order:
All the Part A applications
The Part B application
Copy of first two and last two pages of the US passport.
Copies of birth certificates for all applicants born abroad.
Proof of Indian origin
Make a copy of all the above documents since you have to submit the documents in duplicate.
Paste one photograph on each application form (original and duplicate) and attach the other 3 with each applicant's Part A application.
Mail all the documents to the Consulate as per the instructions. Indicate on the envelope "OCI Application" in bold letters. Make a note of the registration number (in the form USACIxxxxx) for each applicant.
After mailing, keep checking online (link provided below) to see the status of your application. Once the application is received by the Ministry in Delhi, a file number is posted online. Within 30 days your status should change to dispatched.
After your documents have reached your consulate, go to the consulate with a print out of the online status, your US passport and Indian passport (or PIO card).
At the consulate, a person will collect these and then call you when your OCI stamp is ready. You normally get a visa-like sticker in your US passport and a small OCI booklet. Make sure all the information is accurate. You can also mail your passports if you cannot make it in person.