The majority of doctoral programs require some form of standardized test score, usually the Graduate Record Examination (GRE). Depending on your discipline, you may also need to take a GRE Subject Test in areas such as English literature, biology and chemistry. Check with each department to see what is required.
For the most part, if you are going into a PhD program straight out of college, you will be looking to enter a joint MA/PhD program. In most cases, people finishing terminal master's degree programs, will apply directly to the PhD program.
If you are entering a doctoral program from a master's degree program, you will have to take qualifying exams that test general competency in your discipline. If you are moving to a new school for your PhD, you may have to take a second set of qualifying exams to prove your competency by the standards of another school.
Qualifying grades vary from school to school, but often the average grades and test scores of admitted students are shown on the department website of the program to which you are applying. Order a separate set of your transcripts from each school you attended, and send them with each school application.
You will likely need three letters of recommendation from people familiar with your work. Although some colleges have letter services, it is often better to get a recommendation that is specifically crafted to the individual program to which you apply.
Most American schools require residency or a study visa for foreign students. Check with your department website, or contact the department secretary for more information.