Photo District News (PDN) just published a very good interview with photographer Sara Terry about her experiences in applying for and winning grants. I agree with all of her comments and will add a couple of additional thoughts.
First, remember that while a photographer who is seeking a grant needs the funding to complete her or his project, most foundations that fund photography likewise need photographers to carry out their mission. With rare exceptions, foundations don't do the work of photography themselves - they exist to fund projects that fit within the boundaries of their mission. In short, they need photographers as much as photographers need them. It's the photographer's job to figure out exactly what that need is and then find a compelling way to tell why her or his work helps them carry out their mission.
When applying for a grant, don't just read the application guidelines – study the foundation like you would a sitter for a portrait session. What's behind the profile? What makes them who they are? What are they trying to say about themselves? Every foundation has a history, and knowing that history will help an applicant understand more about what they may or may not fund.
Secondly, every foundation is different, and every program officer at a foundation is different. Period. There is no one size fits all, no common agenda, not even a common application form (well, there are a few, but they're rare). Pay close attention to not only what a specific foundation says it wants but also, when possible, who within the foundation will make the final decision. Did the program officer in charge of photography grants change from last year? If so, looking at past grants may not be so useful. A new person often brings a new point of view, and ultimately in most foundations it's the program officer who makes the final recommendation about who will receive a grant. Do the research on the person involved as well as the foundation overall. LinkedIn is a good place to find out about a person's background and interests. Every little insight can help make a difference.
There are a lot of other tips I can offer, but I'll save them for another day since the PDN interview is such a good baseline source of information. Sara knows what she's talking about, and she's gotten the grants to prove it.