If I was left out of my husband’s Will, how do I file for my elective to get what is due me as a surviving spouse?

The right of election falls under the NY Estates Power and trust Law (EPTL) section 5-1.1.  I am going to copy that portion of the section here that applies.  It is long but you need to read it.  You need to serve written notice under the law within six months from the date of issuance of Letters testamentary or administration.  I would go down to the appropriate Surrogate's Court and see if they have a form you can use.  Any written Notice by certified Mail should do so long as the information therein complies with the statute.  This is considered estate litigation and you may want to consult an attorney.  Good luck.

(e) Procedure for exercise of right of election.    (1) An election under this section must be made within six months from  the  date  of  issuance of letters testamentary or of administration, as  the case may be. Written notice of such election shall  be  served  upon  any  personal  representative  in  the manner herein provided, or upon a  person named as executor in a will on file in the surrogate's court in a  case where such will has not yet  been  admitted  to  probate,  and  the  original  thereof shall be filed and recorded, with proof of service, in  the surrogate's court in which  such  letters  were  issued  within  six  months  from  the  date  of the issuance of letters.  Such notice may be  served  by  mailing  a  copy  thereof,   addressed   to   any   personal  representative, or to the nominated executor, as the case may be, at the  place  of residence stated in the designation required by SCPA 708 or in  such other manner as the surrogate may direct.    (2) The time  to  make  such  election  may  be  extended  before  its  expiration  by an order of the surrogate's court from which such letters  issued for a further period  not  exceeding  six  months  upon  any  one  application.  If  a  spouse  defaults in filing such election within six  months from the date of issuance of such letters, the surrogate's  court  may  relieve the spouse from such default and authorize the making of an  election within the period fixed by the order, provided that  no  decree  settling  the  account  of the personal representative has been made and  that twelve months have not elapsed since the issuance of letters.    An  application  for  relief  from a default and for an extension of time to  elect shall be made upon a petition  showing  reasonable  cause  and  on  notice to such persons and in such manner as the surrogate may direct. A  certified  copy  of such order shall be indexed and recorded in the same  manner as a notice of pendency of an action in the office of  the  clerk  of each county in which real property of the decedent is situated.    (3)  The  time  limited  in  this  paragraph for making an election is  exclusive and shall not  be  suspended  or  otherwise  affected  by  any  provision  of  law,  except  that  the surrogate may, in his discretion,  permit an election to be made in behalf  of  an  infant  or  incompetent  spouse at any time up to, but not later than, the entry of the decree of  the  first  judicial  account  of  the  permanent  representative of the  estate, made more than seven months after the issuance of letters.