To change your marital status from married to divorced, you must file an application for divorce with the Superior Court of Justice. This involves at a minimum filling out a court application, paying your fees to the court and having it issued, served on your spouse and then filed with your affidavit of service at the court. If uncontested after 30 days you can then proceed to file your affidavit of divorce and a judge will be given your documents and in most cases will grant your divorce.
There is no way to get divorced simply by living apart from your spouse or outside of the court system. You will not be able to remarry without following this procedure.
After filling out the applicable court forms (available at the court or online), you need to present the court with your original marriage certificate. If you were married in another country you should apply for an original or certified copy of your certificate. If your certificate is not in English you will need to have it translated by a certified translator. If there is a good reason that you cannot get a certificate, for example the country where you were married will not provide you with a certificate, then you can inform the court of your efforts and ask to be allowed to proceed without a certificate.