How does a foreign director get an Indian digital signature?

Through a licensed certifying authority in India, which issues a digital signature certificate after checking identity documents and usually a short video verification. Foreign directors send notarised and apostilled passport and address proof, because India applies the Apostille Convention. Every director signs the incorporation forms with this certificate.

Certification and apostille

Source: Status table: Apostille Convention, Hague Conference on Private International Law (HCCH)