The Foundation Center website has a number of free, helpful guides and tutorials for those new to the grant seeking process.
I recommend starting with the Introduction to Fundraising Planning course, which requires quick and easy registration. This introductory course will get you thinking about your organization’s strengths and how to develop a fundraising plan that maximizes those strengths.
The Guide to Funding Research is a good next step. This course gives an introduction to the world of philanthropy for non-profits, covering such things as what foundations are, who gets foundation grants, and how to find foundations that will fit your organization’s needs.
For a quick introduction to the actual process of writing grant proposals, try the Proposal Writing Short Course. It took me about an hour to work my way through the material, and by the end I had a solid checklist of the steps involved in researching and writing a proposal.