The Office of the VP of Research and the libraries have put together a bunch of search tools to help you find grant opportunities. Many of these resources are best used in combination with their e-mail alerts to update you to new grants in your subject areas.
There are many databases to explore, but good ones to try are: IRIS, SPIN, and Community of Science. Also don't forget to search for grant opportunities in internal U of M funding sources.
The library also offers regular workshops on how to search and set-up your alerts in the best databases for scientific researchers. Look for "Grant Funding - Search Tools and Resources" on our Workshop page for the next opportunity to sign up for this free event or contact our outreach coordinator to deliver this workshop to your class or research group.