If you know the tribunal that issued the decision, search that particular tribunal’s website.
International tribunals are similar to a country’s domestic courts in that that they have different jurisdiction to hear a particular type of case.
Probably the best known international tribunal is the UN’s International Court of Justice, which is one of the few courts with general jurisdiction.
Other international courts and tribunals which issue decisions include:
If you do not know the tribunal that issued the decision, or want to make a broader search (eg, by subject), use the Oxford Reports on International Law.