How do we apply for a Corporation

It depends on the State in which you want to incorporate. Usually, Articles of Incorporation are filed with the Secretary of State or official charged with this function. You will also need to follow the corporate formalities under the State Corporation Act, as well as obtain a Federal Employer Identification Number and if appllicable, file for subchapter S status with the Internal Revenue Service. See a lawyer. The ramifications of screwing this up far outweight the nominal cost of getting it set up correctly.