Yes, this is my advice to maximize your chances of getting that grad school, postdoc, or faculty position. Yes, there are differences between these three - pointed out in text below - but actually I think they are pretty similar in a lot of ways. A blog post using 'one sentence mentoring' echoes this sentiment.
A central goal of any application is to first find out what the people who will read it care about, and then to provide evidence that you have these skills/traits: NOT to just say that you have them. I.e. show, don't tell. Avoid making judging statements about yourself or your work (avoid: 'I am hardworking', 'My research is really interesting', etc.).
The application file must be clear and clutter-free, understandable and exciting to the non-expert. I really recommend you have your whole file read by someone who successfully applied for what you are applying for. One of the key skills for anyone to have is to take feedback seriously and work on changing what needs changing.
Start early. When is this?
- Applying for grad school: Start planning your research experiences and mentor connections as soon as you get to college (freshman year). Start finding future grad schools and advisors in the spring or summer before you plan to graduate – i.e. 1-1.5 years before you want to start grad school. Grad school programs usually start in the fall, and application deadlines are typically in November or December the year before.
- Applying for postdoc positions: Start thinking about what your future research niche will be in year 3 or so of grad school. Think about which postdoc experience will best complement your method and conceptual knowledge in year 4. Go to conferences and look for potential postdoc mentors in year 4 and 5; also start looking for places to get postdoc fellowships, and mark their deadlines in your calendar. Start contacting them about a year before you plan to graduate. Ask for suggestions on how to get funding, assuming you will apply for it. Assume you will need several weeks to write a fellowship application. Remember that university offices may be required to sign off on applications, and in those cases will have their own deadlines before NSF/USDA etc deadlines.
- Applying for faculty positions: Most advertisements come out some time between September and January, to hire starting August. Of course you have started preparing what will go into your file (your research record, your niche, your connections) since grad school. But don't underestimate how long it will take to prepare the actual application packets. Since you want to revise your research and teaching statements with feedback once or twice, I recommend starting to write them as soon as you start your postdoc position, or a year in. During the semester you are actually applying, you'll need to also research information about the particular schools you are applying to, your potential colleagues there, and work on a great cover letter and your interview talk. Your postdoc period could be anywhere from 0 to 10 years, but most common are 2-3: that means you are applying in the beginning of your second year (assuming you started in a Fall semester). Don't delay planning this until the last minute.
The number one thing that people care about is your research record; this should be the main topic of the file (for any of these application types). The main evidence of a great research record are the number of publications and the quality of the journals. What should this look like?
- Applying for grad school: What matters for research experience is not that you came up with the idea for the research – in fact this is on average not a good idea. What matters is that you actually got results and that you can describe these results and their implications broadly, professionally, and expertly without saying you don’t know why you did something or that it was part of what the grad student/advisor/whoever wanted to do. You must find out what the publication plans are for each of the projects you were involved in. Make sure you mention which if any of the research you participated in will be published in your statement, explicitly mentioning the author list (even if you are not a coauthor). Only list publications that you will be a coauthor on on your CV, but do list those even if they are ‘in prep’. Having any is great. List any meetings/conferences/events where you presented research, either as talk or poster, even if they were local events at your school. Remember to also read this.
- Applying for postdoc positions: By the time you apply you will most likely not have all your graduate work published. But it will be necessary to have at least some work published or accepted in journals. It is normal to have anywhere from 1-5 papers published by the time you apply; more would be exceptional. By the end of your PhD, having 5-10 published or submitted is great. In any case mention all the work 'in prep'.
- Applying for faculty positions: Depending on how long ago you finished your PhD, committees will expect the above plus about 1-2 papers/year since finishing. At this stage, quality (which journals, and what is said in the letters about your work, as well as what the committee itself knows about your work) will start to matter more than just the number of publications. However, expect that competitive applications for faculty jobs at good research universities typically have 10-20 papers published, sometimes more.
The second most important thing will be your letters. Any committee reviewing your application is more likely to read your letters than your publications. Observe rules for getting recommendation letters! The letters are what communicates to non-experts what the relevance and quality of your research is; they also impart information like whether you are a likeable person or hard to work with. Your grad school advisor and postdoc advisor will be writing letters for you for a long time yet - so pick the right ones, and then honor the rules of that relationship. Recommendation letters that praise your independence, great projects, and teamworking ability are good; outstanding letters will talk about how your work has already had high impact, and how much potential you show for being a major figure in the field in the future.
Other more specific points:
Applying for postdoc positions. If applying for an advertised position, emphasize that you are a great independent capable innovative scientist, but also that you are a team player and give credit to your prior adviser. Emphasize any links between your expertise and previous projects and the advertised project. Come up with specific ideas relating to the advertised project but do not give the impression that you want to go off and do something other than exactly what the project demands. If you are applying for your own fellowship, expect this to be competitive; but unlike in the previous case, your future mentor is now your ally. Let her read and re-read your application. Do not assume she will know anything or remember anything about the specific call you are applying for; keep on top of the details, read the instructions meticulously. But in every case of doubt, check with your mentor about how the instructions are to be interpreted. Ideally sit down in one or two in-person meetings to go over the process, instructions/RFA, formalities and over the research proposed. Assume that this application will have to be a highly polished document which, other than you, two people have read in detail and provided feedback on everything from content to formatting, spelling etc.
Applying for faculty positions: More than in the previous cases, the people reviewing your file (primarily the search committee) will not be experts in your area of research. Therefore, the broader relevance of your research must be crystal-clear in the document, i.e. your plans and previous results must be exciting, answering fundamental questions in biology, and sound cool. What must also be crystal-clear is what is yours rather than your adviser's; in particular, when you start your own independent position, what will be your research niche that isn't already occupied by your previous mentors, but that is directly following from your previous work. Your plans for the future matter more here than they did before, also. Rarely new faculty are hired who say they will start a completely new direction from their previous work. Mostly committees want to see that you have plans for 2-3 larger projects that can each lead to one grant proposal and several papers in the near future (no more than 2-3 years into your new position). Remember you are supposed to have data collected for around 6-12 papers by the end of year 4 or so into your position. So, you need to have a coherent, feasible, and exciting plan.
Also, on the research statement: by this time there should be some substance (publications), perhaps divided up into 2-3 major topics. I recommend subheadings and attractive images of cool study organisms or results graphs. The search committees are real people: they get bored and/or tired and reading a visually attractive document that uses layout, figures, and headings to lead the reader to the most relevant points will make them happy and better at understanding your work.