The laws governing the legal use, storage and carrying of firearms are constantly changing. Below are the applicable laws in the State of New York as of 2/13/2013. The below information is designed to be a guide and not the final word. If you have specific questions, please refer to  the State of New York legislation at public.leginfo.state.ny.us.

The State of New York will issue a Non-Resident Permit under the same eligibilty requirement set for a Resident Permit.

Eligibility
No license shall be issued or renewed pursuant to this section   except   by   the  licensing  officer,  and  then  only  after investigation and finding that all statements in a proper application for a license are true.
No license shall be issued or renewed except for an applicant
(a)  twenty-one years of age or older, provided, however, that where such applicant has been honorably discharged from the United States  army, navy, marine corps, air force or coast guard, or the national guard of the state of New York, no such age  restriction  shall apply
(b)  Of good moral character.
(c) Who has not been convicted anywhere of a felony or a serious offense.
(d) Who has stated whether he or she has ever suffered any mental illness or been confined to any hospital or institution, public or private, for mental illness.
(e) who has not had a license revoked or  who  is  not  under  a  suspension  or ineligibility  order issued pursuant to the provisions of section 530.14 of the criminal procedure law or section eight  hundred  forty-two-a of the  family  court  act.
(f)  in  the  county  of  Westchester, who has successfully completed a firearms safety course and test as evidenced by a certificate of completion issued in his or her name and  endorsed  and affirmed under the penalties of perjury by a duly authorized instructor,  except  that:
1.  persons who are honorably discharged from the United  States army, navy, marine corps or coast guard, or of the national guard of the state of New York, and produce evidence of official qualification
  in firearms during  the  term  of  service  are  not  required  to  have completed those hours of a firearms safety course pertaining to the safe use,  carrying,  possession,  maintenance  and storage of a firearm; and
  2. Persons who were licensed to possess a pistol or revolver prior to the effective date of this paragraph are not required to have completed a firearms safety course and test.
(g) Concerning whom no good cause exists for the denial of the license.
No person shall engage in the business of gunsmith or dealer in firearms unless licensed pursuant to this section. An applicant to engage in such business shall also be a citizen of the United States, more than twenty-one years of age and maintain a place of business in the city or county where the license is issued.  For such business, if the applicant is a firm or partnership, each member there of shall comply with all of the requirements set forth in this subdivision and if the applicant is a corporation, each officer there of shall so comply.

Applications
(a) Applications shall be made and  renewed,  in  the case  of  a  license  to  carry  or possess a pistol or revolver, to the licensing officer in the city or county, as the case may be,  where  the  applicant resides, is principally employed or has his principal place of  business  as  merchant  or storekeeper; and, in the case of a license as  gunsmith or dealer in firearms, to  the  licensing  officer  where  such  place  of  business  is located. Blank applications shall, except in the city of New York, be approved as to form by the superintendent of  state  police.  An  application  shall  state  the  full  name,  date of birth,  residence, present occupation of each person or individual  signing  the  same,  whether  or  not he is a citizen of the United States, whether or  not he complies with  each  requirement  for  eligibility  specified  in  subdivision  one of this section and such other facts as may be required  to show the good character, competency and integrity of each  person  or  individual  signing  the application. An application shall be signed and verified by the applicant. Each individual signing an application shall submit  one photograph of himself and a duplicate for each required copy  of the application. Such photographs shall have been taken within thirty days prior to filing the application. In case of a license  as  gunsmith  or  dealer  in  firearms,  the photographs submitted shall be two inches  square, and the application shall also state the previous occupation  of  each  individual  signing the same and the location of the place of such  business, or of the bureau, agency, sub-agency, office or  branch  office  for  which  the license is sought, specifying the name of the city, town  or village, indicating the street and number and otherwise  giving  such  apt description as to point out reasonably the location thereof. In such case,  if the applicant is a firm, partnership or corporation, its name,  date and place of formation, and principal place of  business  shall  be  stated.  For such firm or partnership, the application shall be signed and verified by each individual composing or intending to  compose  the  same, and for such corporation, by each officer thereof.
(b)   Application   for   an exemption under paragraph seven-b of subdivision a of section 265.20 of this chapter. Each applicant desiring  to obtain the exemption set forth in paragraph seven-b of subdivision  a  of  section 265.20 of this chapter shall make such request in writing of  the licensing officer with whom his application for a license is  filed,  at  the  time  of  filing such application. Such request shall include a  signed and verified statement by the person authorized to  instruct  and  supervise the applicant, that has met with the applicant and that he has  determined  that,  in his judgment, said applicant does not appear to be  or poses a threat to be, a danger to himself  or  to  others.  He shall include  a copy of his certificate as an instructor in small arms, if he  is required to be certified, and state his address and telephone number.  He shall specify the exact  location  by  name,  address  and  telephone  number  where  such  instruction will take place. Such licensing officer  shall, no later than ten business days after such  filing,  request  the  duly   constituted   police  authorities  of  the  locality  where  such  application is made to investigate and ascertain any  previous  criminal  record  of  the  applicant pursuant to subdivision four of this section.  Upon completion of this investigation, the police authority shall report  the  results  to  the  licensing  officer without unnecessary delay. The  licensing officer shall no  later  than  ten  business  days  after  the  receipt  of  such  investigation,  determine  if  the applicant has been  previously denied a  license,  been  convicted  of  a  felony,  or  been  convicted  of  a  serious  offense, and either approve or disapprove the  applicant for exemption purposes based upon such determinations. If  the  applicant  is  approved  for  the exemption, the licensing officer shall  notify the appropriate  duly  constituted  police  authorities  and  the  applicant.  Such  exemption  shall  terminate if the application for the  license is denied, or at any earlier time  based  upon  any  information  obtained  by the licensing officer or the appropriate police authorities  which  would  cause  the  license  to  be  denied.  The applicant   and appropriate   police   authorities   shall   be notified  of  any  such  terminations.