According to Restatement of the Law (Third), the Foreign Relations of the United States, section 102(2), "Customary international law results fom a general and consistent practice of states followed by them from a sense of legal obligation." The last part of this determination is key - the practice must follow from a sense of legal obligation rather than simply as a courtesy or for some other reason.
Sources for researching customary international law can be quite broad. Some nations, including the United States, publish materials that state their practices in given areas, and these are the most authoritative sources for what is a custom. Additionally, participation in treaties as well as national laws are evidence of a state's customary practises. Because it is almost always best to start with a secondary source when researching customary international law, this research guide focuses on those sources.
For more information on this topic, see the Globalex guide
According to Restatement of the Law (Third), the Foreign Relations of the United States, "General principles common to the major legal systems, even if not incorporated or reflected in customary law or international agreement, may be invoked as supplementary rules of international law where appropriate."
There is no separate research strategy for general principles, per se. In the end, you will be looking for the laws and customs of the world's major legal systems, but as it is almost always impractical to begin your research in this area. It is best to begin with other secondary and primary sources, such as treaties, customary international law, international case law, and scholarly works to see if "general principles" have been previously delineated. If you must begin from scratch, you will simply be researching the law of foreign jurisdictions. For that, please consult our guide, Researching Foreign Law: An Introduction.