What are the legal requirements? 

The legal requirements varies for different types of business (see Q7 for different types of businesses).

You have to figure out whether an auditor is needed.

You have to register the enterprise.

You must consider how you should finance the start-up phase?

More information
Which type of business (form of incorporation) you choose to start is of great importance regarding liability, risk, tax, rights and duties. https://www.altinn.no/en/start-and-run-business/planning-starting/

To register a sole proprietorship, you must choose a business name and describe the business you intend to run. You can find what the requirements for starting a sole proprietorship are, and how to proceed with the registration of the enterprise here. https://www.altinn.no/en/start-and-run-business/planning-starting/registration-of-the-enterprise/starting-and-registering-a-sole-proprietorship/

You can find the requirements for starting a Private limited companies (AS), and how to proceed with the registration here. https://www.altinn.no/en/start-and-run-business/planning-starting/choosing-form-of-incorporation/private-limited-companies/

You can find the requirements for starting a General partnerships (ANS/DA), and how to proceed with the registration here. https://www.altinn.no/en/start-and-run-business/planning-starting/choosing-form-of-incorporation/general-partnerships-ansda/

Figure out whether an auditor is needed:
Any organization that is obliged to submit audited its annual accounts must have an auditor. Whether or not you are subject to the audit obligation will partly depend on your organizational form and the size of your enterprise. https://www.altinn.no/en/start-and-run-business/accounts-and-auditing/do-i-need-an-auditor/

Registration of the enterprise:
How to register your business depends on which company you want to start. You can find more information about the type of company and what is required here: https://www.altinn.no/en/start-and-run-business/planning-starting/registration-of-the-enterprise/

Financing the start-up phase:
Financing a business means obtaining enough capital to set up and run your business. Appropriate financing will help make the start-up period and the early period of the business easier for you, enabling you to meet your payment obligations. https://www.altinn.no/en/start-and-run-business/planning-starting/before-start-up/how-can-i-finance-my-start-up-phase/