Many if not most artists do not immediately get full-time work as a performer/artist. "Arts" is, of course, a very broad term - graphic designers find work in their field much more readily than independent visual artists who paint, or sculpt, ... So some of the answer depends on your field. If you design the visual or musical elements of electronic games, you may well find work relatively quickly. If you are an independent ceramicist, it is likely to take time before you have a large enough clientele to pay the bills.
So let's say that your field is not one that is currently in demand by companies that seek specific creative skills. As a performer, you would seek venues to perform: coffee houses, small regional theaters, local orchestras and bands. You may form your own group whether musical or dramatic, and perform as often and broadly as possible. Artists may band together to arrange shared studio space. To pay the bills, you will need to find other work that fits into your artistic life: one musician I know is also a very fine carpenter - he can take on work that fits within his performance schedule.
Since most performance takes place in the evening or weekend, day jobs are an option - preferably in an area connected to your art: in music stores, book . stores, doing the support work in theaters and concert venues. Artists might seek steady work in galleries, museums. Working in a related area keeps you in touch with the arts world in which you hope to work full-time. And don't overlook teaching: private lessons in any of the arts has not only supported artists for centuries, but can afford a schedule flexible enough that you can arrange your time to keep your own artistic work central.
And look around broadly to see whether a career outside the arts has appeal; a surprising number of entrepreneurs and executives have an arts background. What has made them successful is the ability, learned from their arts experience, to think creatively and problem solve "outside the box." Some of these people perform on the weekends or keep up their studio work, but have found satisfaction in business and manufacturing as well.
The bottom line: investigate the possibilities as broadly as possible, so that you choose with "full malice of forethought." Make a long-term plan and have the patience and faith in yourself to follow it. Know that most successful artists have begun with a period of struggle - and some remember it as the most creative period in their lives.