Research what schools offer doctoral programs in your field. Discuss your future plans with professors from your Master's program, as they should have doctorates in the field and should be familiar with the process for doctoral students in your subject. Also research the school's faculty specialties. Doctoral students are assigned a supervisor to guide them through the doctoral thesis-writing process. Schools tend to assign students to supervisors with experience in the student's research field.
Visit and tour the school and the department you will be studying in. Doctorates are primarily research degrees, so tour the research facilities on campus, either laboratories, libraries or research centers. Talk to the university faculty about heir knowledge and how it can help your future research.
Complete the requirements for admittance to the schools of your choice. Each school may require different things, such as a certain grade point average at the Master's level, published research, a certain minimum GRE score or other requirements. While these may be the minimum requirements, having more than the minimum will make you stand out against the other applicants to the program.