There is no central international body that creates public international law; it is created by several sources.
The Charter of the United Nations is the establishing document for the International Court of Justice (ICJ) as the principal judicial organ of the UN. Article 38(1) of the Statute of the International Court of Justice lists the sources that the ICJ uses to resolve disputes as follows:
1. The Court, whose function is to decide in accordance with international law such disputes as are submitted to it, shall apply:
a) international conventions, whether general or particular, establishing rules expressly recognized by the contesting states;
b) international custom, as evidence of a general practice accepted as law;
c) the general principles of law recognized by civilized nations;
d) subject to the provisions of Article 59, judicial decisions and the teachings of the most highly qualified publicists of the various nations, as subsidiary means for the determination of rules of law.
Further information regarding these sources is provided in this Research Guide under the headings and links listed below:
Prior to the practice of negotiating multilateral treaties after WWII, international law consisted primarily of customary rules. Custom has evolved through a long historical process by which state practices and recognition of the binding character of those practices have become normative rules. The rationale for custom is that it rests on the consent of sovereign or equal states. The creation of custom can be slow and its content uncertain, and it has been replaced to a large extent by multilateral treaties, but custom nontheless continues to contribute significantly to international law. (Source: Gillian Triggs, International Law: Contemporary Principles and Practices (LexisNexis, 2nd ed, 2011)
Customary international law consists of rules that derive from "a general practice accepted as law" and exist independent of treaty law. Unlike treaties, customary international law is not written. To prove that a certain rule is customary, 1) there must be objective evidence of state practice and 2) the international community must believe that such practice is required as a matter of law - this subjective element is known as opinio juris (as formulated by the Court in the UK case West Rand Central Gold Mining Co v The King  2 KB 391). The criteria for the two elements required to identify custom were articulated in the 1969 North Sea Continental Shelf Cases (FRG v Denmark; FRG v The Netherlands). See the official reported judgment - North Sea Continental Shelf, Judgment, (1969) ICJ Reports 3.
The work of the International Law Commission (ILC) provides authoritative evidence of customary law.
At its 70th session in 2018, the International Law Commission adopted 16 draft conclusions on identification of customary international law. The Draft Conclusions explain how to identify the existence and content of a rule of customary international law by ascertaining whether there is a general practice that is accepted as law (opinio juris).See the ILC's website on its work on the Identification of Customary International Law, which includes all reports and the final outcome. See also commentary on the ILC Conclusions and the history of the doctrine of customary international law in Jean d'Aspremont, 'The Four Lives of Customary International Law' (2019) 21(3/4) International Community Law Review 229–256 (open access on SSRN).
The following will help you research international custom:
General Principles of Law
The 'general principles of law as recognised by civilized nations' have been traditionally recognised by courts as a source of international law, using judicial reason and logic to abstract the normative rule. See for example the decision of the PCIJ in the Chorzow Factory (Indemnity) case (1928) PCIJ Series A No 17
The writings of jurists are important in describing and analysing evolving norms and identifying general principles of law. In the absence of decisions of international tribunals, the body of international legal doctrine depends on the articulation of jurisprudence in books and journal articles.
Sondre Torp Helmersen, 'Finding "the Most Highly Qualified Publicists": Lessons from the International Court of Justice' (2019) 30(2) European Journal of International Law 509–535. Available on open access from OUP.
Sandesh Sivakumaran, 'The Influence of Teachings of Publicists on the Development of International Law' (2017) 66 International and Comparative Law Quarterly 1-37. Available on open access on SSRN.
Oxford Bibliographies Online - International Law (University of Melbourne staff and students access only) provides authoritative encyclopedic entries and annotated bibliographies on a range of topics such as general customary law and general principles of law.
The Max Planck Encyclopedia of Public International Law (University of Melbourne staff and students access only) contains comprehensive and authoritative overviews of all aspects of international law. Entries are arranged alphabetically by topic under broad subjects such as sources of international law, customary international law, general principles of international law, state practice and the law of treaties.