If you apply for non-academic jobs, particularly those outside your current field of research, you will need references that differ in some ways from academic ones. Those differences will affect whom you ask to provide references, how you help prepare your referees, and how they submit their references for you.
Whom to ask. Academic references include your advisor (thesis / dissertation supervisor), and usually committee members and faculty members who have taught graduate courses or supervised your teaching. References for non-academic jobs may come from all of those people but if possible should also come from someone who can speak to your skills most relevant to the job you’re applying for. If those are research skills, you may not need people other than your academic referees; if you are applying on the basis of skills developed outside your graduate work, ask someone who can speak to that work to provide a reference. A good rule of thumb is to have three to five referees, speaking either to work within your current educational timespan (graduate school) or to relevant experience not gained in graduate work.
Frequently graduate students tell me that they fear asking their advisor for a reference for a non-academic job, worrying that they will no longer be taken seriously for academic positions and that their non-academic reference will be prejudiced. If you believe this may happen, you should do some research before speaking to your advisor. Ask someone your university’s career services office, if it works with graduate students, or your department’s graduate director, or your department’s chair, whether your advisor is likely to be sympathetic to your non-academic job search. The best person to ask is probably a student from your department who got a non-academic job. You may find more sympathy and help from your advisor than you imagine. If your advisor is not supportive of your non-academic search, you will be able to explain why you don’t have a reference from him or her to an interviewer for a non-academic job, and you will sound (and be) credible.
What is different. Academic references are typically written in advance and submitted as needed; non-academic references are more likely to be submitted via a phone call or an online form specific to that job application, and the information asked for will vary more from non-academic job to job than from academic job to job. You will need to ask your referees how they would prefer to be contacted to be asked for a reference (email? work or mobile phone?), because they may not be able to just hit “send” on what they have already written or placed on file for you. You should have this contact information for all your referees when you start applying for non-academic jobs.
Once you get to the reference-supplying stage of a job application, requests for references for non-academic jobs will typically have shorter deadlines for submission than for academic posts, postdocs, or fellowships. In addition, these requests will not necessarily follow the academic job-search calendar of applying in the winter or spring, say, for postdocs that begin late summer or early fall; instead, they will be asked for each time you get to the reference-checking stage. Once you assemble a list of referees, you need to let the academics among them know that they may be contacted for references at non-standard(-to-them) intervals.
If one or more of your referees are out of pocket while you are applying for jobs (on leave, or spending time between terms doing research in remote locations), ask if they will be available to submit references during that time. If they are not, you can explain why to the person asking for the reference. If this is likely, you should probably have five rather than three referees.
Prepare your referees. Because your academic referees will be providing references further outside their area of expertise than they will for academic jobs, you need to provide them with some information about the job, more than in a casual conversation: “oh, you’re applying for [standard postdoc]?” They need an up-to-date copy of your résumé, a copy of the job description for which you are applying, and any notes from phone screens or interviews you have already have. They need to know the deadline for submitting the reference, or when to expect the call. You may send a reminder 24-72 hours before the call or the deadline.
Surprises. Unlike academic references, non-academic references, especially those given over the phone, are occasionally taken by someone in recruiting, human resources, or a junior-level employee before the hiring manager reads the transcript. Academics recommending graduate students for jobs are used to speaking as authorities to other authorities, and may find speaking to a young or low-level employee disconcerting. Sometimes phone references are recorded (the person taking the reference will say so, if that is the case), which academics also occasionally find disconcerting.
Good news. As a general rule, references carry less weight in non-academic job applications than they do in academics, though they are not unimportant. Once you start a non-academic job, your performance in that job for that employer instantly becomes more important than whatever you did in graduate school, and you will start immediately creating a new set of people who can provide references for you.