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 nonetheless 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 [1905] 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:
Researching Customary International Law, State Practice and the Pronouncements of States regarding International Law - research guide from Globalex by Silke Sahl.
Researching customary international law (to be updated in 2024) - this open access tutorial from the Institute of Advanced Legal Studies by Hester Swift provides an overview of the key print and online sources for researching customary international law. It covers finding evidence of state practice in the records of states' foreign relations and diplomatic practice, and in legislation concerning international obligations. It also looks at researching the practice of the UN Security Council, UN General Assembly and UN human rights committees.
See also:
Custom's Future: International Law in a Changing World by 
The Changing Nature of Customary International Law : methods of interpreting the concept of custom in international criminal tribunals by 
Sources of State Practice in International Law by 
Customary International Law in Times of Fundamental Change by 