This is a firsthand account of my experiences, impressions, and thoughts dealing with the postdoctoral grant process. When I wrote my application (which ended up being funded), I was a mid-second-year postdoc in a cardiology unit affiliated with the Department of Medicine and College of Medicine at a state school in New England. I came there with a Ph.D. in molecular physiology and biophysics and no grant-writing experience.
WHY WRITE A GRANT APPLICATION?
Submitting an application was a great opportunity to practice doing the very things that could make or break a career--my career! I decided to pursue a postdoctoral grant largely to fulfill as many components as possible of what I considered constituted a successful academic postdoctoral experience.
My list, in no particular order, is to publish papers, give presentations at meetings, learn a valuable (obscure) laboratory skill, become associated with cutting-edge work, and prove to all out there that I can get research funding.
Looking more closely, I feel that writing a postdoc grant provided me with several positive experiences:
I learned how to organize a research question and show that funding the project would clearly be an excellent use of the agency's money. I proved that I can successfully obtain research funding. The best evidence that you can do something is to have already done it. I ingratiated myself to the boss. (I assume that covering a good portion of my own salary is viewed favorably by my employer.) Postdoctoral salaries being what they are, getting your own grant may also enable you to try and negotiate a raise. (Surely I jest.)
I learned how to organize a research question and show that funding the project would clearly be an excellent use of the agency's money.
I proved that I can successfully obtain research funding. The best evidence that you can do something is to have already done it.
I ingratiated myself to the boss. (I assume that covering a good portion of my own salary is viewed favorably by my employer.) Postdoctoral salaries being what they are, getting your own grant may also enable you to try and negotiate a raise. (Surely I jest.)
For these reasons, I felt that writing a grant was something I wanted (and needed) to do. My boss was supportive of this endeavor, although I never felt like my position in his lab depended on my getting the grant.
My next tasks were to decide on the research question and then decide to whom I would submit the application. These steps required the most work!
Unless you have a desire to alienate your mentor, it might be wise to write a postdoctoral grant that includes a research question related to his or her research. Because my boss is the head of a cardiology unit, this meant the cardiovascular field was open. I decided to direct my work into areas in which the lab and I had experience--why put up more hurdles than needed? Therefore, I focused on finding a research question in cardiology that examined heart failure or cardiomyopathy and ended up deciding to use isolated rat hearts to study cardiac function.
Because I had been exposed to this type of research when I started in the lab, I used the techniques I'd learned to study a type of cardiomyopathy in a model different from the one being researched in the lab. Having experience with existing models and techniques allowed me to report preliminary results I had obtained up to that point. This showed that I could physically perform all the techniques outlined in my grant and that they were successful in generating data.
Once I decided what problem I was going to address, I had to begin the complex process of looking for funding. (Your strategy will depend upon your individual situation). I decided to pursue an independent research track, meaning that I would not be studying a subtopic of my boss's grant. Although this gave me a chance to exercise my critical-thinking muscle, it also placed me as a lower priority on the boss's radar.
I can honestly say that I don't know if this was the best decision. I had done an "independent" project for my Ph.D., so I was somewhat prepared, but independent research involves a great deal of autonomy, and sometimes I wished there were intellectual support for my work. I did incorporate smaller aspects of my boss's grant into my grant, which I think garnered support because it was familiar.
My experiences in the medical funding world put me at the wrong career stage for any National Institutes of Health  (NIH) grants. There are grants available for more senior postdocs or for those with degrees conferring the right to treat patients, but I was a relative rookie with just a Ph.D.
The NIH Web site for extramural research is reasonably helpful, although it could help more with finding appropriate grants. I perused the Web pages describing their grants section without any real guidance (that is, I didn't talk to anyone at NIH). You may come across something that looks like it fits your requirements.
I also contacted my university's office of sponsored programs (OSP). However, be prepared for little real help; the employees may generally be midlevel paper shufflers who, in their defense, are unable to be "experts" on funding from specific organizations or in specific disciplines. But these people will be signing things later, so put on a happy face! I found myself having to get signatures from the OSP both before and after I got the grant, so it is best to always leave as many bridges standing as you possibly can.
I looked at Hughes fellowships and came away with the impression that there is money for predoctoral students, medical students, and just-minted M.D.s. But the Howard Hughes Medical Institute  Web-based grant page is a perfect model for the NIH; you plug in some facts and it tells you the grants you can get! I'm serious, they actually help you find out what grants you qualify for, which appears to be an exception to the rule.
Then I looked to the American Heart Association  (AHA). They provide postdoc fellowships that are designed for the development and support of "individuals before they are ready for some stage of independent research"--they fit the bill quite nicely. I called the national center and asked them to send the forms.
The forms turned out to be well organized. I first read through the forms and found out whose signatures I needed and then checked to see that they (or someone able to sign for them) would be around when the ink needed to meet the paper. Only then was I ready to put my ideas out there.
My boss helped edit the application but focused more on the research question's phrasing than actual content. In hindsight, I wish I had been more patient. I should have written a full rough draft of my research plan and gone over it myself at least a couple times. I only did one draft before letting the boss hack away at it, and that just did not allow me to really smooth the writing out to make sure it sounded right.
Once I was finished writing, I was ready to get the signatures. Various university paper shufflers have to sign, so my advice is to put on your walking shoes and go-- don't use university mail; it's way too slow. Last but not least, be ready to make 25 or so copies of the whole application. Paper jams and copier failure are to be expected, so give yourself more than 30 minutes to run to the nearest copy center!
With only one grant under my belt, I am not an expert on the do's and don'ts of grant writing. Your supervisor should help refine your grant, but try to do as much as you can on your own. I started writing about 2 months before the deadline and dropped down to a day or two of benchwork per week--I spent the rest of the time writing.
I find you can only write well a certain number of hours per day (five or six, tops) and only for so many days in a row, so the bench break was helpful. Hopefully you will only have a few years of postdoc work, so use this time to learn from others' experience while developing your own process and style.
Be aware that doing any kind of animal work requires written courses in animal handling and surgery! You also need approval before animals can be ordered. These things take time, especially because the courses your institute offers may only meet every month or two or at the beginning of each semester-- so plan ahead. The paperwork involved in using animals is endless--for example, just for doing surgery, we have surgery forms, recovery logs, animal use forms, and anesthetic use forms.
My general advice for laying out the grant is to focus. Start with an established experimental model, and try to envision specific papers you know can result from the proposed experiments. As a postdoc, you are not ready to spend the time to sell a new model to investigate a particular area; rather, look at areas that have been mentioned or hypothesized as critical to a question, or adapt a proven model to fit your grant. Finally, as I've been told, "publications are money in the bank"; strive to put money in the bank.
I'm now finishing up my third year and writing up the first paper from this grant. I should have another around the first of the year if the data gods are nice to me. I'm going to apply for another grant but will be careful not to let that interfere with getting these papers out first.
The grant-writing process should be a useful learning experience--it has been for me. As a postdoc, your position should not depend on your getting the grant. Rather, it should be a chance for you to begin your career. Good luck!