In order to form a corporation or limited liability company (LLC), you must file a document with the Secretary of State. Although the format of the documents from state to state is generally the same, states differ in the names of the documents. For example, in California, the document to form a corporation is called the Articles of Incorporation, and the document to form an LLC is called the Articles of Organization. In Texas, the document is called the Certificate of Formation in the case of both corporations and LLCs.
By filing the required documents, you will be providing the state with basic information about the company. Such information will include the name of the company, the company's purpose, the name and address of the organizer, the name and address of the registered agent, the names and addresses of the directors/members, and information about shares to be issued (if any).
If you are forming a partnership, no state filings are required to form a general partnership. However, if the liability of one or more partners will be limited (i.e. a limited partnership), formation documents are required to be filed with the state. In addition, all partnerships are required to file a tax return every year.