Take your graduate exam early enough that you can retake it if need be (e.g., summer before senior year rather than that fall).
Determine general application requirements (e.g., graduate vs. law school).
Begin to narrow your schools. GRE, etc. will ask for schools to which scores should be sent.
Begin drafts of essays, and select writing sample.
Phase Three (fall of senior year)
Narrow your schools--talk to professors, look through list of faculty, ask to talk with present graduate students, consider location and cost of living, ask for rates of placement of graduates and attrition rates, consider specifics of programs (e.g., How are comprehensive exams or papers handled? Do you teach as part of program?).
Polish letters and writing sample.
Request letters of recommendation early. (Give drafts of application materials to your recommenders.)
Send out applications in November/December. (Remember transcript requests.) Note international deadlines if any.
Be aware of deadlines for fellowships (particularly internal fellowships) as well as applications. Apply for financial aid (FAFSA)--needed for many scholarships.
Phase Four (generally, spring of senior year)
Visit schools--talk with professors and students, ask about housing, on-campus work, and insurance, ask about graduate assistantships.
Weigh final school options--talk with UST faculty, family, etc.
Make decision before deadline (generally, April 15). Do not be afraid to ask respectfully for time to consider multiple offers.
Let the Philosophy Department and other students know so that we can celebrate with you, give you any last minute tips, perhaps even find you help to move (e.g., split costs with another student headed to same area).