The process is:

1. Visit any Aadhaar Kendra of your convenience.
2. Carry valid Indian Passport with you
3. Fill details in the enrolment form
4. Giving Email ID is mandatory for NRI
5. The declaration for NRI enrolment is slightly different. Read and sign the same in your enrolment form
6. Ask the operator to enrol you as NRI
7. Give your Passport as Proof of Identity
8. You may choose to use your Passport itself as Proof of Address and Date of Birth proof or give some other valid document/s for this (As per https://uidai.gov.in/images/commdoc/valid_documents_list.pdf)
9. Complete the biometric capture process
10. Check all details on the screen (in English and the local language) before you allow the operator to submit
11. Collect the acknowledgement slip/ enrolment slip that has your 14 digit Enrolment ID and Date & Time Stamp. You can check the status of your Aadhaar from https://resident.uidai.gov.in/check-aadhaar

Refer Government Portal ( https://uidai.gov.in/) for more information