A company may be formed in three ways under section 3 of the companies Act, 2013:

1. Private Company– Section 2(68) of the companies Act gives the definition of private company. A private company is any company which (1) restricts its member’s right to transfer their shares (2) limits the maximum number of members to two hundred and (3) most importantly prohibits any invitation to the public to subscribe for any of its shares. It can be formed with two or more persons as members.
2. Public company– Section 2(71) of the Companies Act defines Public company as any company which is not a private company. It can be formed as seven or more persons as members.
3. One Person Company– Section 2(62) of the Companies Act defines One person company as any company which has only one person as a member. 

STEPS REQUIRED FOR THE INCORPORATION OF A NEW COMPANY

Incorporation is a legal process used to form a Corporate entity or a Company. It involves drafting of legal documents that list the primary purpose of the business its name and its location and the number of shares and class of stock being issued, if any.
The Companies Act, 2013, lays down the following rules for the incorporation of both the public as well as private Company. As per section 3 of the Companies Act, 2013, in case of Private Company at least 2 members are required, whereas in Public Company, 7 persons are required and in case of One person Company, 1 person is required.
Step-1
Filling the proposed name of a Company for approval to the Registrar of the Company (ROC)
According to sec. 4(2) of the Act, a Company cannot be registered with identical name or resemble too nearly to the name of an existing company registered under the Act.

As per section 4(4) of the Act, the person can make an application to propose the name of the Company to be registered with fees as may be prescribed.
Upon receipt of the application, the Registrar on the basis of information and documents furnished along with the application, may reserve the name for a period of 20 days from the date of approval of the said application. Provided that in case of change of name by any existing company, the Registrar may reserve the name for a period of 60 days from the date of approval.
Step -2
Obtaining Director Identification Number As per sec. 153 of the Act, every individual intending to be appointed as Director of the Company shall make an application for allotment of Director Identification Number in form DIR 3 to the Central Government with prescribed fees.
Step- 3
The Company must have to select the name of persons who will act as Director.
Step-4
Drafting of Memorandum of Association (MOA) The Memorandum of Association is the Constitution of the Company
which must contain the basic information of the Company. The purpose of MOA is to enable the members of the Company, its creditors and the public to know what its powers are and what is the range of its activity.
A pr Rule 13 of the Companies (incorporation) Rules, 2014, Memorandum of Association must be signed by every subscriber along with address, description, occupation, if any, in the presence of atleast one witness who shall attest the signature and shall likewise sign and add his name, address, description and occupation, if any.

The memorandum of association of a company shall contain the following particulars under section 4 of the companies Act, 2013:

1. Name of the company
2. State in which registered office of the company is located
3. Objects for the formation of the company
4. The liability of all the members of the company
5. The amount of shares with which the company is to be registered and the names of the members subscribing for the shares of the company
6. In case of one person company, the name of the person, who will become the member of the company in event of death of the subscriber

Step- 5
Drafting of Article of Association (AOA)
Article of Association which is an important document explain the operation of the company, purpose for which Company is incorporated along with the information for the process of appointment of Directors and also management of the financial record of the Company

The articles of the association of the company shall contain the following particulars under section 5 of the companies Act,2013:

1. Regulations for the management of the company
2. Provision for entrenchment to the effect that the certain provisions of the articles may be altered only when conditions and procedures as restrictive as special resolutions are complied with
3. The provision for entrenchment may be added either at the time of formation of the company or by a special resolution in case of a public company and an amendment in the articles agreed to by all the members, in case of a private company.

Step-6
Registered Office As per section 12 of the Companies (Amendment) Act, 2017, the Company on and from 30 days of its incorporation and at all time thereafter must have registered office capable of receiving and acknowledging all communication and notices as may be addressed thereto. The Company shall furnish to the Registrar verification of its registered office within a period of 30 days of its incorporation in such a manner as may be prescribed.
Step- 7
Application for Incorporation of a Company According to section 7 of the Companies Act, 2013, an application shall
be filed with the Registrar within whose jurisdiction the registered office a Company is proposed to be situated in Form no. INC.2 (in case of One person Company) and Form no. INC. 7 (in case of public and private Company) along
with fees as provided in the Companies (Registration office and fees) Rules, 2014 for registration of a company.
Step-8
Issue of certificate of Incorporation
The Registrar, on the basis of the documents and information filed, shall register the name of the Company and issue a certificate of incorporation in the prescribed form (FORM no. INC-11) to the effect that the proposed Company is
incorporated under this Act. On and from the date mentioned in the certificate of incorporation issued, the Registrar shall allot the Company a Corporate Identity Number (CIN) which shall be distinct identity for the Company and which shall also be included in the certificate.

In order to form a new company, the promoter shall furnish the following documents with the Registrar of Companies within whose jurisdiction the registered office of a company.

1. Memorandum and Articles of Association of the company
2. A declaration by the director, manager or secretary of the company and from each of  the subscribers to the memorandum that all the requirements of this Act in respect of registration has been complied with and contains information that is correct and complete.
3. Address for correspondence, particulars of name and other particulars of every subscriber to the memorandum along with proof of identity.

Apart from furnishing the above mentioned documents, the registrar of companies may ask for any other information as may be required by him for satisfying himself with respect to the authenticity of the promoters and the company.