The first thing you need to know is that there is no such thing as international copyright protection. As discussed in the Copyright Basics section, copyright in the U.S. happens automatically and immediately as soon as you create something in a "fixed, tangible form." That doesn't mean, however, that your copyright is necessarily protected in other countries as well or in the same way or for the same length of time as in the United States.
Each country has its own unique copyright laws that govern intellectual property (like copyright) in that country. So, a certain country's copyright laws only apply to works created and used in that country. This means that the copyright you hold in the United States is not valid in other countries in the same way that our other laws don't apply to people in other countries and vice versa. Other countries may have different rules for what gets copyrights, who gets copyright, how long copyright lasts, or other restrictions.
Some countries do, however, have treaties with one another that agree on how they will recognize each others' copyrights. Thus, if you hold copyright in the U.S. and want to see what sorts of rights you have in Japan, you should see what if the U.S. and Japan have any treaties that relate to copyright.
Generally speaking, you must obey the law of the country you’re in and in some cases you must also obey the law where the servers are located.
It is often a good idea to think about the law of the country which will be most impacted by what you were doing (if you’re creating a website that will be heavily used by citizens of another country, for example), and try to follow relevant international laws.
There is often confusion in the US about fair dealing (in the UK and most Commonwealth countries) and moral rights (in the EU).
Fair dealing is not the same as fair use. There are no fair use provisions in most international law. Fair dealing tends to be much more specific about how you can make educational use of material.
Moral rights are generally not recognized in US (except in very specific circumstances), though they part of the Berne convention and also widely part of the law in many countries.
In some countries, particularly in the EU, databases can also be protected. So, when using or creating databases for use in other jurisdictions beyond the US, there may be some additional copyright protections to be aware of.