As with finding any foreign law, Google carefully.
Similar to researching legislative history for U.S. laws, it is a good idea to find other documents used in the preparations for treaties or produced during treaty discussions and negotiations. These types of documents and related discussions are often called travaux preparatoires and can be found in preparatory documents, such as working papers, and in commentaries.
To compile this information, you may have to search for individual documents. For example, U.N. General Assembly debates or U.S. Senate document reports. This will depend solely on the treaty you are looking for. If you're really lucky, these materials may already be compiled for you, either in books or in journal articles. Here is a non-exhaustive list of common places to find important travaux preparatoires and compiled sources. See a reference librarian if you have questions or trouble navigating.
If relevant to your research, remember to search for any national implementation of a treaty. There may be some domestic legislation required by a country, which must be implemented, to make the agreement effective. Similar to the discussion on Working Documents above, you may also find it helpful to consult legislative history regarding implementing legislation.
For example, after becoming a party to the European Convention on Human Rights, the United Kingdom passed the Human Rights Act 1998 as "An Act to give further effect to rights and freedoms guaranteed under the European Convention on Human Rights; to make provision with respect to holders of certain judicial offices who become judges of the European Court of Human Rights; and for connected purposes." Human Rights Act 1998, c. 42, http://www.legislation.gov.uk/ukpga/1998/42/contents.