A proprietorship/sole trading firm is a business that is owned and run by an individual person. The owner and the business are treated one and same. Proprietor is personally liable for all business debts i.e his personal property may also be used to repay business debts.
Proprietorships are not regulated by any particular Act, hence there is no registration. Every buiness needs registration under Shop & Establishment Act whether it is providing a service or dealing in goods. Other registrations such as GST etc depend upon nature of product/service.