One of the best ways of learning how to write successful grant applications is to volunteer for opportunities to serve as a grant application reviewer.
In some instances, this strategy may be easier said than done, but the energetic grant writer will actively seek out grant reviewing activities.
NIH grants are perhaps the most selective (both in successful application as well as in securing positions as a reviewer).
However, the NIH Office of Extramural Research offers valuable information about successful grant application writing. Its description of the Peer Review Process is very detailed with numerous supporting documents.
The NIH Center for Scientific Review provides guidelines for peer review meetings, and it also provides a portal for those interested in volunteering as reviewers.