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There is no single way for researching foreign domestic law (i.e.outside of UK) as legal systems, sources of law and the availability of legal materials vary greatly from country to country. If you are planning to research foreign domestic law, it is a good idea to consult with secondary sources first so that you can familiarise yourself with its legal system, locate primary sources and build research strategies. You should also be aware that many resources for foreign domestic law are not translated in English. If you are not familiar with the language, you will need a realistic expectation on how much resources you could access.
Here are some resources where you can find some basic information on the country you are researching such as legal systems, primary sources, etc.
Oxford Reports on International Law (ORIL) contains reports on over 5,500 cases across public international case law, reporting on international courts, domestic courts and ad hoc tribunals. Case reports contain the full text of each decision, headnote, as well as analytical commentary.