The process for an international adoption involves several steps. Though not comprehensive, here are the general steps common to most international adoptions.
The specific steps you will need to take vary by state, country, adoption agency, and if your child is considered a special needs child.
If adopting outside of the United States, please check out the State Department's information on adoption. There, you can find current adoption news, detailed information on the countries you may choose to adopt from, statistics on orphans from various countries, and information about international rules and regulations as defined by the Hague Adoption Convention.
While all the red tape required when adopting an orphan from a foreign country might seem cumbersome, the regulations set in place are to not only protect you, but also protect children from exploitation through illegal adoption operations that, sadly, still exist throughout the world.
Read about international adoption and get country-by-country overviews and requirements at the Adoptive Families site.