Below I've listed several websites and some books for you to find and research the opportunities that will best serve your needs. Another great place to find opportunities is on the CV of your friends and colleagues. Ask them about their experiences and the application process!
Bridget Riley, About Yellow (2014-2013), Oil on linen 64 1/8 x 109 7/8 inches (163 x 279 cm). (© Bridget Riley 2014. All rights reserved. Courtesy David Zwirner, London.)
Art Opportunities Monthly: Yearly subscription service for access to grants and other opportunities.
Artist Trust: Artist Trust is a nonprofit organization dedicated to supporting individual artists working in all disciplines throughout Washington State.
Artwork Archive: Complete Guide to 2019 Artist Grants & Opportunities
Cranbrook Academy of Art's List: Grants and Other Funding Sources for Individual Artists (with grants listed by region and discipline)
Foundation Grants to Individuals Online: Foundation Grants to Individuals Online is the ideal resource for students, artists, researchers—subscription service.
Grants.gov: Federal grants
National Assembly of State Arts Agencies: State arts agencies directly serve the public through grants for artists, arts education, organizations and communities.
National Endowment for the Arts: The National Endowment for the Arts is an independent federal agency that funds, promotes, and strengthens the creative capacity of our communities by providing all Americans with diverse opportunities for arts participation.
Regional Arts and Culture Council
The following is a subjective list of "big name" grants—awards that have name recognition and often, big prizes to accompany their prestige.
Niki de Saint Phalle (1930-2002), Je t’aime, Colored lithograph Stamped signature 1971.
20 Top Artist Grants and Fellowships You Might Actually Be Able to Get | Bloun Info (2012)
7 Individual Artist Grants That Will Make You Stop, Drop and Apply | Artwork Archive
36 Amazing Art Grants To Apply For Today | Format (2018)
Battenfield, Jackie. The Artist's Guide: How to Make a Living Doing What You Love. Cambridge, MA: Da Capo Press, 2009.
Rosenberg, Gigi. The Artist's Guide to Grant Writing: How to Find Funds and Write Foolproof Proposals for the Visual, Literary, and Performing Artist. Watson-Guptill Publications: New York, 2010.