Before beginning a search, consider what qualities you (as a department and/or as a committee) require in a candidate, and what qualities you desire in a candidate. Use this information to write an honest position advertisement; the way in which the ad is written will strongly affect the applicants and applications you receive. Be sure to consult with an Affirmative Action or Equal Opportunity Officer if you have one at your institution. Advertise on the AMS's Employment In the Mathematical Sciences webpage.
Timelines for searches vary widely, but these panelists prefer deadlines from late November to early January. Many committees initially cut their applicant list down to their top 10 - 50 candidates by early December, followed by a round or two of discussion to trim the list to 10 - 30 candidates to be phone interviewed or interviewed at the Joint Meetings. Campus interviews then take place in February and March. Be aware that if your committee's timeline is significantly different from this range, then you may have trouble either in getting a candidate to accept an offer early, or in finding acceptable candidates remaining in the applicant pool.
Funding for advertisements and budgets for attending the Joint Meetings and conducting campus interviews are generally somewhat flexible, and usually paid for by Dean's offices or other upper-administrative offices. Start asking at the Dean's level for this information.
If your administration and budget allow, attend the Joint Meetings to do preliminary interviews. Avoid the Employment Register (computer-scheduled interviews) but embrace the Interview Center (self-scheduled interviews). Allocate 1/2 - 1 hour per candidate, and have at least two department members present per interview.
Phone interviews are useful after the Joint Meetings to help determine the list of campus interviewees. (If you don't go to the Joint Meetings, phone interviews are a good substitute; if you do attend the Joint Meetings, then you may wish to do phone interviews with very promising candidates who did not attend.) Many committees use phone interviews as a way to gauge the depth of a candidate's interest in their institutions. It's best if you can alert the candidate (by email) that you'll be calling. Be sure to mention the time in both your time zone and the candidate's time zone, if they differ.
You should arrange for the candidate's housing and meals during his/her interview. Some committees arrange travel in conjunction with the candidate; others ask the candidate to make arrangements and get reimbursed after the interview.
Campus interviews have many purposes. Chief among them are: assessing the candidate's teaching and research skills; determining fit with the department, institution, and students; giving the candidate enough information to assess the position. Research skills are generally assessed by having the candidate give a research talk, or by relying on letters of recommendation. More difficult seems to be assessing teaching skills; you can have a candidate teach a class or give a general undergraduate talk, though neither is really ideal. We recommend against trying to assess a candidate's teaching skills by viewing a research talk. Determining fit is generally done by having the candidate meet as many people as possible and then getting feedback on the meetings.
Using feedback from all quarters, the committee should come up with an ordering of the candidates to use in making offers. Often department heads or deans actually make the offers and do all the negotiating. Your search may not be over at this point, because you may be called on to answer questions during the negotiation process, and your top candidates may turn down offers.
Supporting new hires is important both for retaining new faculty and helping them get tenure later. It is common for new faculty to receive teaching load reductions in their first year. If you can, assign a mentor (either from within or outside the department) who is willing to answer many questions. Talk to the dean about supporting a Project NExT application, and ask the new hire if s/he is interested (s/he should be!) Take care of these matters before the school year ends, and you'll have completed a successful search.