Make a short list of the top programs in your field. Use a combination of peer recommendations, professor recommendations and media rankings to produce such a list. Be careful when making your list; a top-rated overall school may be weak in a certain subject, while a weak school may be strong in one or two subjects. Ask your professors which schools have the best experts in the fields you want to study.
Acquire a copy of your undergraduate/master's transcript. Call your school's registrar or academic information office about obtaining this information. Not all doctorate programs require undergraduate grades, but some do, so you must have a copy of your transcript ready. If your school handed out grades on the online self-service page, print a copy of each semester's grades; you can use this until your official transcript is mailed out.
Sign up for a Graduate Record Examination (GRE) preparation class. Register by visiting the website of one of the companies offering GRE courses and signing up for a course in your area. Even if you already have written the GRE and obtained a good score, you want as high a score as possible when trying to get in to a top Ph.D. program, so paying for a prep test and re-taking it is well worth the money.
Sign up to take the GRE test. Register online at the Educational Testing Service (ETS) website by providing your name, address, demographic information and payment information. Choose a date a few months from after you complete your prep course, giving you enough time to study and hone your skills.
Contact college professors and ask them for references. Contact your master's thesis supervisor and instructors. Or, you can contact the college professors with whom you got your best grades.
Write a statement of purpose for submission to each school on your short list. Look up the "ideal candidate qualities" mentioned on each school's website for Ph.D. program admissions. Write a short, one-page statement for each school, outlining why you wish to attend its program and why you would be a good candidate. Each statement of purpose should be tailored to the specific school; however, all should contain a paragraph on your academic career and a paragraph on your research interests. About 500 words, including the introduction, conclusion and body, is ideal for a statement of purpose.
Submit necessary information to each school before its admissions deadline. At most schools, this is around March or April; however, it can vary. Download the application form from each school's website. Send each school a package containing your application form, your transcript, your reference letters, your statement of purpose, your work samples (i.e. master's thesis), your GRE scores and your contact information. Send this to each school's admissions office, either by attaching scanned pages to an e-mail, or by sending the package out by regular mail.