The process of registering a private limited company in India involves obtaining a Digital Signature Certificate and Director Identification Number, choosing a unique company name, filing the application for incorporation with the Registrar of Companies, paying the necessary fees, and obtaining approval. Once the company is registered, directors can apply for a Permanent Account Number (PAN) and Tax Account Number (TAN). The entire process usually takes around 10-15 days and it is recommended to seek professional help for a smooth registration process.