Many organizations offer funding to artists based on demonstrated merit in an application process. New York Foundation for the Arts (nyfa.org) provides a searchable database for artist awards offered by a variety of organizations all over the country. You can search for "cash grants" and read about each group's eligibility requirements, deadlines, and prizes. You will also find links to their websites. Many fellowships and grants have specific eligibility requirements; make sure you fit these specifications before applying. For example, New York Foundation for the Arts offers an Artist Fellowship specifically for artists living in New York state. To apply for any of these grants or fellowships, you will usually need to submit a portfolio with digital images of your work, as well as an artist statement or statement of purpose.
Residency programs provide temporary studio and living space, allowing artists to focus on their work within a community of dedicated artists. Though some of these programs can be expensive, many offer fellowships or grants, or charge no fees at all. The MacDowell Colony, for example, charges no fees (macdowellcolony.org), and the Vermont Studio Center offers a limited number of full fellowships each year (vermontstudiocenter.org). Several websites offer comprehensive searchable databases of artist residencies, and provide information on qualification criteria, location, size, and notable alumni. Look at the Worldwide Network of Artist Residencies (resartis.org) and Alliance of Artist Communities (artistcommunities.org) for possibilities.
Searching for awards and fellowships requires patience; the application processes are very competitive. Make sure your application and portfolio are presented well. Finally, be persistent and keep looking for opportunities.