Forming and organizing a corporation involves several steps:

Choose a business name: The name of your corporation must be unique and cannot be already in use by another business. It is a good idea to check with your state's secretary of state office to make sure the name you want is available.
File certificate of formation: You will need to file a certificate of formation (aka articles of incorporation in certain states) with your state's secretary of state office in order to create your corporation. This document typically includes information about the corporation's name, purpose, and stock.
Appoint directors: A board of directors is responsible for overseeing the management of the corporation and making major business decisions. You will need to appoint the initial directors of your corporation either when you file your certificate of formation or shortly thereafter.
Issue stock: A corporation is owned by its shareholders, who own shares of stock in the corporation. You will need to issue stock to the initial shareholders of your corporation.
Create corporate bylaws: Corporate bylaws are a set of rules that govern the internal management of the corporation. You will need to create bylaws for your corporation and provide copies to the shareholders.
Hold an organizational meeting: An organizational meeting is a meeting of the directors to adopt the bylaws, elect officers, and conduct other business. You will need to hold an organizational meeting for your corporation.
Obtain any necessary licenses and permits: Depending on the type of business you are operating, you may need to obtain specific licenses and permits in order to legally operate your corporation.
Register for state taxes: You will need to register your corporation for state taxes and obtain a federal employer identification number (EIN).

Once you have completed these steps, your corporation will be formed and ready for business.