Westminster College has changed to Westminster University! See my updated contact information.
Astronomers, check out the Career Resources on the Careers page of the AAS website! These resources are curated by your volunteer AAS Committee on Employment.
Also check out Career Resources from the Society of Physics Students website.
The NSF AAPF will be one of your first postdoc deadlines, and it will be the longest application you write. Don’t be turned off by the length and deadline of the NSF. Defining your research and expressing it clearly and early helps your future applications go more smoothly.
I think the only compelling reason to not apply to this, if you are a US citizen applying to other postdocs in general, is if you don't care at all about the education/outreach component. A half-hearted broader impacts portion will not fly for this fellowship. I don't mean you need a lot (or even any) experience, just that you need to be genuinely interested in doing the work you propose.
Keep in mind that *all* NSF grants are judged both on Intellectual Merit and Broader Impact. If you plan to continue in the field and successfully apply for NSF grants in the future, you will need to fulfill Broader Impacts, so might as well start now!
More on Broader Impacts (because that is what most people worry about):
Utilize existing resources/infrastructure at your proposed institution. What is there to help you reach your intended audience - an education research group, a planetarium, a university or department outreach coordinator, etc. The less logistic work you need to do, the more you can focus on accomplishing your goals. And you demonstrate to the committee that you are for real.
Know your goals: Doing outreach by showing random people pretty astronomy pictures is nice but probably doesn't do much. Are you trying to improve scientific literacy, in whom? Improve the diversity of scientific workforce? How, by improving recruitment or retention? (There is plenty beyond these examples) If you have not previously thought about these things, research what interests you.
Research statement: "tell them what you are going to tell them, then tell it to them, then tell then what you just told them." Make it extremely easy for reader to "get the point" - they read hundreds of pages.
General note: I did not realize before application season just how much "cold calling" (or emailing really) I ended up doing. As an introvert this was intimidating. For people that feel that way, keep in mind a professor has nothing to lose by signing off to say "yeah, if you get this fellowship, we can collaborate." They are allowing someone else, the fellowship committee, to decide, there is no point in them judging you. Even for fellowships that you don't win, aka almost all of them, you have made a new professional contact and you are "on their radar"
For astronomers: You'll want to look beyond just the AAS Job Register for ads, especially from physics departments. Even ones specifically looking for astronomers might not post on AAS. You can create email alerts for jobs on sites like HigherEdJobs.com, Vitae from the Chronicle of Higher Education, and California State University Careers.
Many colleges are very sensitive to being someone's "back up plan." They will want to be extra sure that you want the job and that you know what you are getting into. Some small departments may not have done a faculty search for decades; this is a big investment for them.
Know the environment. If you've only studied/worked at large research universities, try to visit a SLAC and spend some time getting to know the faculty and students. It is a very different environment.
In particular, research may not be nearly as important to getting the job as it would be at a larger institution. When proposing research projects, make sure they are achievable with undergraduate students and with the resources available at that institution.
If your university has some kind of certificate in college teaching, do that.
Teach. In addition to TAing, look for opportunities to teach your own class, e.g. during summer sessions or at a community college.
Have faculty observe your teaching. Most applications will request that two of your three letter writers be able to comment on your teaching ability.
Educate yourself on pedagogy. For your application, you will need to write a teaching philosophy, and this will help ground your ideas in well-established research on teaching and learning. Attend workshops on teaching and learning through your institution and your professional society (AAS, ASP, APS).
Educate yourself on diversity, equity, and inclusion. Many applications will ask you to specifically address this. Even if you do not have experience working with a diverse population of students, being familiar with the literature and the issues faced by underrepresented students is important. "Diversity" doesn't mean "students who like math and students who don't like math."