The Grant Writing Academy at Stanford offers many resources for graduate students delving into the world of grant writing. Their website will help you navigate the many stages of preparing, writing, and submitting a grant proposal.
Their Grad Funding page has a list of links to lists of funding opportunities for graduate students, postdocs, and faculty, focusing on federal agencies, such as NIH and NSF, as well as nonfederal agencies, such as societies, foundations, and associations. Check out the list of links to see if you qualify for any of the opportunities listed!
Although designed to support students in the sciences, the resources found here can be applied to students in many different disciplines.