So, here are some tips. Feel free to add your own.
Perhaps you know, when you start the application process, exactly what you want your disseration to be about. If so, great. Look where the people in your area are located. Write to them. Find out who you would like to work with. Apply there.
Method two is mentor leading to topic: In your coursework, you'll have a variety of courses, and will get to know other students. Find a professor who you like, and check if he/she is a good mentor. Then figure out what that professor is interested in, read up about it, and propose something. EVERY article ends with "further research is needed".....find some that your favorite prof thinks is needed.
2. Putting together a committee. a) Be sure to have someone on the committee who knows the departmental rules down cold. Which style manual. Who gets copies when. What paperwork is needed when, and so on. b) Be sure to have no feuds on your committee. Academic departments are filled with petty jealousies and rivalries. Keep them off your committee. c) NO loose cannons. Many departments have some assistant professor who thinks the way to tenure is raising all sorts of tricky issues. Or a professor WITH tenure who has odd ideas. Keep them off your committee.
Start thinking about your committee EARLY.
3. Choosing electives. To the extent possible, every elective should be useful for your dissertation.
4. Writing. Be sure to remember that a dissertaion is NOT the great American novel, nor is it your lifework, nor is it intended to be the greatest piece of scholarship ever.
5. Consultants. Many departments allow, or even encourage, the use of consultants for technical issues. I do this sort of work myself (in statistics for social science types). This isn't cheating (unless you don't get it approved). Your research has to be your own, but you can get help.
Well, that's what I can think of right now. Chime in with questions, or more suggestions, or whatever.