Who is eligible to apply for instructor or assistant professor positions? I am a math PhD student in my last year, and I've been on mathjobs.org looking for jobs.

I see a lot of jobs for instructor positions, or jobs titled "assistant professor", where the main work load seems to be teaching undergraduates and no research. 

It seems that the main qualifications are a PhD. I am confused on what kind of applicant is qualified to apply. It seems that I am qualified enough to apply, assuming I receive my PhD by the time the job starts, but I am worried I am being naive. I do realize that someone that has already had an instructing position, or "assistant professor" position previously, or experience as a postdoc, would look better than a fresh PhD.

Are these jobs typically given to PhD's that have been through a few postdocs, or do PhDs straight out of grad school have a fair enough chance at getting the job? 

To be blunt, am I wasting my time applying for these positions?
No, you are not wasting your time.  For assistant professorships at colleges with little or no research component, you should feel free to apply in your last year of a PhD program.


  I do realize that someone that has already had an instructing position, or "assistant professor" position previously, or experience as a postdoc, would look better than a fresh PhD.


In my experience that is not necessarily the case.  In my PhD program, probably more graduates go on to this type of job than any other career trajectory.  Many of our graduates do get tenure track jobs straight out of graduate school.  Getting such jobs later after doing a temporary position is still possible, but it seems to me that the chance goes down.  Even top twenty liberal arts colleges still hire many assistant professors straight out of grad school.  Obviously they could select candidates with postdoctoral / visiting faculty experience.  They often choose not to.  I would go so far as to say that in many teaching jobs, postdoctoral experience could be viewed as a bit of a mismatch.

(An old friend of mine has written an article about the pleasures of being a visiting faculty member.  To a certain degree it contradicts what I said above.  But I think he is more looking on the bright side of taking multiple visiting positions than suggesting that they are necessary.)

Three more comments:


You should know that an "instructor" position is typically very different from an "assistant professor" position.  Suffice it to say that if you want an assistant professor position, you probably do not want an instructor position.  In many math departments, there are recently hired instructors with PhDs teaching alongside of instructors without PhDs who have had the job for a longer period of time.  This is not saying good things about the current job market.  In my opinion, having a PhD makes you overqualified (and certainly, underpaid) for most instructorships, but of course it's up to you to decide on what's worth your while.
Rather than further academic training, what you want to have in order to get these jobs are a strong teaching record and excellent teaching abilities in an interview / model classroom situation.  Many PhD programs nowadays provide opportunities for their students to display these credentials.  If you are looking for a primarily teaching job post-PhD, I hope you have been doing everything in your power to acquire these credentials during your graduate career: in many cases, this provides the best opportunity to do so.  (If you are not sure where you want to go on the teaching/research perspective, I hope that you have erred on the side of acquiring more of these credentials than you will necessarily need.)
When it comes to individual departments, Nate Eldredge made a good suggestion: you can look through CVs of recent (and less recent) hires to see what their credentials are.  However, a small department may have a small sample size.  Nowadays many (most?) people on the academic job market apply to on the order of a hundred jobs; necessarily this includes many jobs for whom the goodness of fit is unknown to them.  Not applying to jobs because you are worried that you might not be competitive does not seem like a good strategy when so many other strong candidates are applying for everything in sight.  You don't have to stuff envelopes anymore (like I did when I was applying for jobs less than ten years ago!), so the differential amount of work in applying to some positions that you fear might be a stretch but don't know is small.  When in doubt, apply.  I say this as someone who reads through hundreds of applications a year.  If we're not interested, then we're not interested, but it's no problem.