As a companion to my college and graduate school advice pages, I decided to write one for job applicants as well. This comes from my own experience as an applicant, search committee member, and search committee chair. Some of this advice is probably specific to finding a tenure-track math job at a small university that values teaching, but much of it should apply more generally.

• Apply for every position that you might want to accept. Not everyone is hiring every year, so look around. If you thought college and grad school admissions were tough, now you're applying against hundreds of other candidates at a school that is likely going to hire just one person. A really competitive college or graduate program may accept 5-10% of applicants. A typical hiring process will accept closer to 0.5% of applicants.
• Definitely search EIMS and MathJobs. I'm not going to provide links since if you can't find them on your own, then you're already in trouble.
• If there is a place you really want to be, go directly to jobs section of their web site. It also doesn't hurt to contact the department chair to ask if they might be hiring. The answer will likely be something like "definitely not this year, not sure about next year" but at least then you'll know. Or it could be that a position is about to be advertised as soon as one more administrator gets back from overseas to give it the final approval. You'd be amazed how much work goes into the process before the job ad can appear.
• Along those lines, the job ad may say some things that are higher priorities than others. If you don't fit the description perfectly (e.g. the ad says an algebraist is preferred, but you're a topologist, or the ad calls for postdoctoral experience and you're just finishing grad school), go ahead and go for it if you really want the job (with emphasis on your work in algebraic topology, or courses for which you were the instructor of record), but if you don't fit at all (e.g. a Ph.D. is required and you are nowhere near earning one) then don't waste the committee's time.
• If you are finishing graduate school and applying for tenure-track positions, keep in mind that you are going up against postdocs and even more experienced applicants. No matter how good you are now, you will likely be a stronger candidate for those positions in a few years, so don't be discouraged if you have to take a temporary position for now.

• I cannot stress this enough, READ WHAT THE JOB AD ASKS FOR. If it requests a cv, cover letter, teaching statement, research statement, and letters of recommendation, and you just send a cv, your application will probably never even reach the search committee. If you are missing just one piece and the rest of your application is strong, then they might contact you to ask for the last piece, but mathematicians are supposed to be able to follow directions literally.
• If applying discreetly (no letters and requesting that your references not be contacted until the last minute), make sure to be upfront about this and make sure it is ok. Just omitting references will not work out well for you.
• Proofread all of your materials, and have someone else proofread them for you.
• The importance of the cover letter cannot be overstated. This is the part of your application that is unique to each job you apply for (or at least it should be!). Really great candidates might get away with a generic cover letter, but responding to details from the job ad and showing that you know something about the school and the department will make the committee WANT to read the rest of your application. Better yet, they will likely want to talk to you, thus getting you to the first-round interview stage.
• Why are you leaving your current position? If you are graduating, then this is obvious enough that it probably does not need to be said. If you are finishing a postdoc, then it need only be briefly mentioned. What concerns me is applicants who are currently in a tenure-track position and give no indication of why they are applying elsewhere.
• If you are in a large graduate program, make sure you emphasize how you stand out from the rest of your class. There was one school in particular where I kept noticing letters on the same stationary, with professors writing similar recommendations for multiple students, and so many students had won teaching awards that it was all just meaningless.
• If you get an interview, make sure you have some questions to ask. Obviously you want a job, but you have to show an interest in this one in particular.
• The overriding message here is that hiring is like a courtship. No matter how wonderful you are, you need to show a real interest in the school for them to pick you above all the other wonderful candidates.

• Do not get a reference letter from someone else who is applying for the same job. Similarly, do not agree to write a reference letter for someone who is applying for the same job.
• Do not list on your cv the job offers that you have rejected.
• Do not send an incomplete application. If something causes your application to submit before it is ready, figure out whom you need to contact to get the rest of your files in there. A technical glitch will not be counted against you, but ignoring it will.
• While using LaTeX is highly recommended, make sure you know how to use it. Default margins and quote marks going the wrong way are rookie mistakes that indicate you are not yet ready for a permanent job in the field.
• While customizing your cover letter to each job is great, make sure you send the right one. The committee does not want to read about how excited you are to be somewhere else.
• Make sure your cover letter fits the job. If all you talk about is how devoted you are to your research, then I'm not going to consider you for a 4/4 teaching load. A research postdoc and a liberal arts teaching position probably require two completely different letters.
• Also along those lines, keep it professional. Relevant personal details may be appropriate, but I remember reading one letter that got creepy when we realized that none of us knew the candidate at all.
• If interviewing at the JMM, be in contact via email and/or cell phone. If you miss your scheduled interview and don't say anything about it for hours, then the search committee has learned all they need to know about you.

• Due to employment laws, parts of the process must remain confidential. The committee does not want to give false hope or discouragement to anyone. If you have another offer in hand, then it is appropriate to contact the search committee chair to let them know and ask if an offer is imminent.
• My own experience was that applications could be sorted pretty easily into 3 categories of approximately equal size: unqualified/incomplete/inappropriate, qualified but not a good fit (a lot of generic cover letters end up here), and those who appear to be a good fit on paper. Those in the last category (as deemed by a subset of the search committee) were then read by more of the committee to narrow the list to about 30 for first-round interviews.
• While attending the JMM is not necessary, it may work in your favor. We did phone interviews for top candidates who were not going, but once we got through the top 20 or so, the remaining slots were filled at the JMM since those interviews are easier to arrange.
• First-round interviews, whether by phone or in person at the JMM, are not likely to result in an offer (you've only talked to a few people, probably for about 30 minutes). This is more of a screening process; think of it as making it to the quarterfinals. The whole committee looked carefully at these candidates, then the interviewers narrowed the list to about 10 semifinalists. Another round of discussion, including notes from the interviews, followed to decide on 3 finalists to bring to campus for full-day interviews.
• Note that at this point there are more factors at work. The dean and perhaps even a VP must approve the on-campus interviews since they are not cheap.
• The on-campus interview is your chance to really get a feel for the school. You will probably teach a class, give a talk on your research, and meet with a variety of faculty, students, and administrators. Make sure you know what your audience will be for the research talk. If it is undergraduates, then the talk should be accessible to them and give a clear picture of what they could work on with you.