You need to show not only that you want the money, but that you need it too. There are different types of funding - core, project, operating and capital funding. What kind of funding do you want. Grants come with conditions. This question particularly applies to government organizations.
Many government agencies get their work done through community groups.
They want to give you money because it's part of their job. This question most applies to private foundations and corporations. They tend to have trends in the type of projects they'll fund. Although their criteria change from year to year, if they've funded something similar in the past it's worth asking them again. Also, you can ask other organizations who've done similar projects where they got their money from - this can makes this process go faster.