The collective FCIL brain trust has produced some fantastic roadmaps for research on foreign and international law, both generally and narrowly on specialized topics. Skimming through a research guide will help you feel more comfortable with the jurisdiction or topic, and save time on finding the right tool for the question. You can also recommend these helpful resources to your patron!
Globalex has research guides on international, comparative and foreign (domestic) law, for nearly every jurisdiction and popular topic. Each guide is written by a librarian or lawyer trained in the topic or jurisdiction, although quality does vary. Some will provide extensive background sections, thorough guides to the law sources, and even annotated bibliographies of key works, while others will be much more perfunctory.
Be sure to click on the "UPDATE" link, if there is one, to get the most up to date version.
While less comprehensive than Globalex, the American Society of International Law's repository of guides has in-depth, methodical, excellently-written guides on the key areas of international law, including human rights, international economic law, and the UN and EU.
LLOC's Guide to Law Online chiefly aggregates links to sources for primary materials, such as government pages and legal information institutes, by country and topic. However, each national or topic page also links to research guides, CRS and agency reports, and other sources useful for research, making it a good stop at the beginning of the research process.
Additional Sources for Guides
Libraries with big foreign law collections also tend to be good at producing research guides, e.g. Georgetown, Harvard, Columbia and Yale in general, and University of Washington for Japan, Korea and China. Biddle currently has guides on human rights, treaties, and rule of law.
There are more extensive manuals on FCIL legal research that provide even more detail on the process and sources. If you have more time or a more complex problem, consult one of these.
In addition to FCIL manuals, Biddle has research handbooks for law students and legal researchers in specific jurisdictions, such as the one for Canada below. It's most likely we will have them for the common law, Commonwealth countries, but we do also have some for other countries. Searching LOLA using "legal research -- [country of choice]" will turn these up.
The Bluebook's rules on international citations, and the country tables in the back, can be a good quick way to figure out where FCIL information can be found. There are a few additional useful citation manuals for other countries as well.