Choose your field or sub-field. Doctoral programs vary from institution to institution and country to country, so having a good idea of what your field is--political science, biology, engineering--will ground your search. Having a sub-field or specialty in mind will also help you determine which specific doctoral programs are right for you. Focusing on a sub-field will also help you narrow down the institutions that specialize in your area of study.
Look at the research being done in your field and determine where it is coming from. A doctorate is meant to make you an expert in a field; choosing a program with faculty that is producing high-quality research will likely enhance your credibility as a scholar. This step will also help you narrow down the institutions that are potentially right for you, and may even help you determine who potential supervisors might be.
Make a list of the best programs and research them carefully. There are too many colleges and universities in the world to consider each and every one as a potential institution for you. List your top schools and proceed to research them--the easiest way is on their websites--and their programs. Ask yourself some guiding questions pertaining to who teaches at the institution, the requirements for the doctorate, the cost to attend and what courses are offered. These questions will help you develop criteria for later comparing the schools.
Ensure that you are eligible to apply and attend the institution. Before making the commitment to visit a school or apply to it, make sure that you meet the institution's requirements for previous education, such as a master's degree. The institution may also consider your previous grades, your language facility and perhaps even your nationality/citizenship.
Determine your top schools and contact them directly. As you narrow your list, you should be thinking about closer contact with the institutions that have kept your interest. Contact potential supervisors, key faculty members, and even the graduate secretary of the department in order to obtain as much information as possible. This can be done over the phone, by e-mail or even in person.
If possible, visit the institution or institutions that you are interested in attending. A doctoral program is a major life commitment, and you need to be comfortable with the institution, the faculty, other graduate students, and the city in order to maximize your chances of completing the program and enjoying yourself while you do so. Chatting with current doctoral students at the institution is a good way to get the inside information on the program.