Long Term Planning, for early in the graduate career:

When you go on the market, you will need:
3 letters of recommendation concerning your research. It is ideal to have one from someone outside BU, so you should try to meet people in your area from other universities. To do this: travel to relevant conferences, especially once you are working on your thesis, speak about your work as often as possible, ask your advisor for help, always go the dinners after colloquia. The Boston area is wonderful in this respect. Attend seminars at other schools.

At least 1 letter addressing your teaching (other than your advisor's, which will cover everything). Have Dick Hall come observe you teaching. Take the opportunity to teach at least one course on your own in the summer. You can also ask someone you assist to watch you give a substitute lecture, and write for you based on that, especially if that person has a reputation as a strong teacher.

Many places only ask for three letters, but a fourth or more will not hurt you. If you have done something interesting out of the ordinary, ask a relevant faculty member to write a letter about it.

You will eventually need to show you are not a clone of your advisor, so think about a second area that interests you and diverges somewhat from his or her interests. You do not need to do any work in this area (yet), (although a paper is great, if you area is conducive to this). At the very least, it will help if you can discuss it intelligently in your interviews. It is also a nice occasion to develop relationships with faculty other than your advisor.

People in statistics especially might look out for summer internships, including ones in corporations, that support their experience/research

Again, speak as often as possible about your work, for the practice as well as for the networking.

In The Final Year; applying for and landing a job.

There are two kind of academic jobs to look for: post-docs and tenure track positions. Post-docs are temporary positions at a prestigious university (in your field) that usually carry reduced teaching and allow you to develop a research program under the guidance of the resident faculty. they are less common in statistics than in math, but are on the rise. Tenure track jobs carry no teaching reduction (usually), but they do eventually lead to tenure, if all goes well. Teaching recommendations are important for tenure-track jobs, even at a school that strongly values research. (The most research oriented schools do not hire fresh PhD's for tenure track positions anyway.)

Deadlines for job applications are in January, so be sure to talk with your advisor in the fall to determine when you will be graduating. The year you graduate, fill out your applications around Thanksgiving to meet the Jan. deadlines, and give your letter writers plenty of time. If you can, give them a preprint or a paper or a piece of your thesis. When sending an application to a university, contact anyone you know at that university. Even if that person is not on the hiring committee, he or she may be able to request that your application be read carefully. If you miss the January deadlines, be alert for temporary positions that open up in March.

BU will mail your application packets for you: you should have all your letter writers from BU forward their letters to Karen Durant, and you should give her addressed manila folders with your cover letter, CV, research and teaching statements, along with any other documents the particular institution wants. She will add the recommendations and mail the whole packet. Try to allow plenty of time for BU mail service. If there is doubt, pay the extra postage.

Getting a job is a two step process: the CV and other materials in the application packet, and the interview. Adjust your application materials to each particular institution you apply to. The faculty are looking for a match, and you can use your CV or cover letter to let them know what about you is especially appropriate to their institution. This is also a chance to show that you have done your homework, and know something about their school (even if this homework is only reading the university and departmental web pages, what you write will change, and can reveal your interest in that particular place). Your application packet should also include the AMS cover sheet, teaching and research statements, and the abstracts of any papers you have written. Take time to write good versions of all these documents, and show them to someone else before sending them out.

For the interviews, one of the best things you can do is practice your lectures beforehand. Develop a talk abut your thesis research that is accessible to undergraduates, and one for graduate students. If you are asked to interview, be sensitive to the intended audience. Take the interview with the dean seriously; he or she has veto power.

Finally, the yearly AMS meeting has a job fair, which is a good place to interview for tenure-track positions. Even if the school you applied to is not participating in the Employment Center, it may have a faculty member at the conference who would be willing to talk with you. The Employment Center is widely and accurately described as a cattle show, but it is an excellent chance to meet people face to face, which will make them more likely to take an interest in your application, as they will already have had a brief chance to assess you in person.

In summary, try to enter your final year of graduate school with some papers accepted if possible, or submitted if not. (However, it is normal to not have done these things, depending on your area of research.) Have an idea of who your letter writers will be, with one from outside BU. Ask or have asked people to observe your teaching, for the teaching letters. The application process takes an amazing amount of time, so start early.