Many PhD programs will have scholarships through the school. These scholarships might be called "fellowships" and will often have requirements like teaching a class or doing research under a doctor.
Check online scholarship search sites. Sites like collegescholarships.org often have a database of available scholarships for all education levels. These are an excellent resource to find scholarships that are both broad and very specific.
Some companies, businesses or private organizations will offer scholarships to PhD students. Usually these scholarships will require some work, interning or written reports.
Check into minority or gender-specific scholarships. There are often scholarships available to minority students or female students that are not available to other students.
PhD scholarships are often granted for specific degrees, such as astronomy or biology. Degree-specific scholarships will often have fewer requirements than other scholarships, though you might need a copy of school transcripts.