Contact the National Endowment for the Arts (NEA) and the National Endowment for the Humanities (NEH) for federal grant information. The NEA offers a number of different grants adding up to hundreds of thousands of dollars. However, though these grants are highly prestigious, there is also a lot of competition for them. A crafty artist might be able to go after other federal grants, though. For example, if the subject of their work happens to overlap with cultural exploration or history they could apply to grants from the NEH.
Contact your local city hall for state and community funding information. States and cities often have their own means of funding the arts. Often, a city is required to spend a certain percentage of their money on community art.
Join your local art centers, committee, or association. These entities strive to reach out to local artists and give them a means of displaying their work. They are a prime place to go if you want to network and find out about local funding opportunities. If you're lucky, there might even be an artist's co-op in your area. Although co-ops usually charge a membership fee, it can be well worth it because of the networking potential and the events that they hold.
Find funding from private grants, estates, and fellowships. Many large estates and foundations have special provisions for funding the arts. However, these grants often have key restrictions placed on them by their founders. Some only service certain cities, others restrict their funding to art with a certain theme. Private grants are a good funding opportunity, but it always pays to check the application requirements to make sure that your art is a good fit.
Participate in art fairs. A lot of artists find that the majority of their money doesn't come from elaborate pieces that sell for thousands of dollars to a museum, but instead from the accrued dollars gained by selling smaller, cheaper pieces to the general public at fairs. Most communities have at least one annual art fair, and sometimes several. Not only can an artist sell a large number of smaller pieces at these events, but they are a prime opportunity for advertising their work. It is also common to receive customized orders at such events. General county and state fairs are also good advertising opportunities, not to mention the potential for prize money.
Contact local galleries about displaying your work. Many towns have galleries dedicated to local art. Some of these galleries are juried, only choosing to display art which has gone through a rigorous selection process. Even so, most of these galleries allow the artist to post price quotes with any piece they submit. Other galleries are purely commercial, serving as an outlet for all local artists to sell their work. These galleries usually charge a commission based on the profits, however.
Check out your local coffee shops, banks, and cafes for potential gallery space. These locals often host a rotating exhibit of local artwork along with pricing information for the entertainment of their clientele. Be sure to leave a stack of business cards with them so that visitors can contact you if they're interested in special orders or other works.
Sell your art online. There are several sites on the internet designed specifically for selling your own art. The downside is that it does not adequately advertise artwork unless the artist buys ad space on other webpages. Also some sites charge a monthly or annual fee while others take a small commission based on sales. If you sell a lot of art, you will be better off with the monthly fee. If you are just getting into the business, it is more cost effective to go with a commission based service.