So I will preface this post by saying that I am not an expert at the NIH system, but I have received funding from NIH and am currently in the process of renewing my grant. Here is some advice for new comers to the NIH system that I wish I had known before starting the process.
1. Find a mentor that has NIH funding and is close enough to your field that they can read proposals and give you pointers. Don't be afraid to ask someone you don't know too well at your institution or another. Most people will say no if they don't feel up to it, but many people will be generous with their time. I find that activities for women faculty is a great way to meet women in other departments/schools who might be willing to serve this role. Keep searching until you find a careful and ruthless reader. You don't want someone who will just correct your grammar you want someone who will tell you what you are doing wrong structurally and how you are shooting yourself down.
2. Learn the NIH funding mechanisms(and lingo) and look for smaller starter grants. R03 (small research grant) and R15 (for institutions with little NIH funding) can be great mechanisms for getting started. There are relatively few of these grants at study section and they are reviewed together, so it is easier to stand out. R21s are OK, but they are high risk/high reward proposals so they need to be a little more innovative than just the first Aim of your future R01. Also the transitional K99/R00 grants are great if you are still a post-doc (and have a year or more to go). These make you very attractive to future employers since you walk in the door with 3 years of funding for your research. I have a friend who used this to leverage a faculty job with reduced teaching.
3. Get a copy of a funded proposal that is close enough to your field you can understand it. Read it and note the structure, what are the key parts, and what strikes you as you read it. Important points need to be reiterated clearly so that they are hammered home.
4. Start writing early. Try to have a complete draft a month before the deadline so you can get critiques from others and have time to modify. I find my best grants get put to rest for a week or so and then picked up and cleaned up before they are submitted. Spend a lot of time on your Specific Aims page. If you haven't sold the reviewer by the end of the first page, you are wasting your time.
5. You need preliminary data. Even when it says you don't, you do. So get to work on those experiments. And, for R01s, that data needs to be published (or at least some of it does). You need at least one publication on the project. And if you have collaborators you are going to put on the grant, you need a publication with them. You need proof that you can work as a team and get research data together that is publishable. NIH is risk averse. You are asking them for a lot of money (> than $1 million for an R01) and they want to know that you will be able to do what you say you will do. Would a VC firm give you a million dollars for that project? No then get more data. (This is some of the tough love one of my mentors gave me and she was right!). Don't waste your time submitting R01s until you have these publications no matter what others may tell you.
6. You should probably be about 1/3 of the way through the research when you submit. That's when you know you have enough data.
7. Make good friends with a business manager/grant administrator who know NIH grants and have them guide you through the forms (it's not fun the first time). Bring them coffee or whatever they like and treat them nicely. People are always yelling about their grants and those who are nice often get the most help.
8. Make sure that your work is hypothesis driven (even thought that's not what the guidelines say). Reviewers like hypothesis drive research and be very clear about how you will measure outcomes. E.g.:We will assess skin healing by x stain at 12 days and expect treatment x to show more skin cells in the wound than in untreated control.
9. Always write a cover letter. Look at the institute within NIH that you think should fund your work and make sure your research falls in their area of interest. Request this institute in your cover letter. Look at the list of study sections that review research in your area (available online). Ask a mentor for pointers here if they have study section recommendations. Look at the members of the study sections. Pick the one you think is most qualified to review your work. When you look at the members you should recognize some names of people whose work you know. If not this is a red flag that you are in the wrong place. Find the right study section for your work. REQUEST THIS STUDY SECTION IN YOUR COVER LETTER. You don't want someone who knows little about your work guessing where it should be reviewed. Guide it to the right place. (PS If you don't like where your grant is assigned, you can appeal your study section if you do it right away!)
10. Remember that almost no one is getting funded the first go around (especially these days). Remember to check that new investigator box and hope for the best. You get one revision (now) so you can use those comments to rewrite and you get an additional section (Introduction) to respond to the comments. If you do a good job of addressing the comments your score generally goes up. Be nice in your response, the same reviewers usually review your grant so offending them will not help your score. Patience is key!
Please leave additional questions in the comments and I hope this was helpful.