First, the artist may be home-based worker. If you satisfied with this, search for jobs on the Internet. You can work remotely: draw comic strips, create cartoon characters or characters of online games, perform illustrations for books and magazines.
In order to work, you have to create your portfolio that reflects your skill. The quickest way of accommodation works – creation site where you can offer potential customers. Besides on the Internet there is information about the contests in which you can participate and show their abilities. Start a blog and offer him the services of a painter and Illustrator.
If the option of home-based work does not suit you, resume and contact those organizations where popular artists. It can be private studios, publishing houses of books, Newspapers, magazines, fashion, decorative workshops, theaters, special educational institutions, where they teach fine art.
In recent years very popular are "related" profession: restorer and designer. But to do this you must get additional education on the chosen specialty and then seek work in restoration workshops, design bureaus, advertising companies.
If you know how to draw portraits, you can try to work on the street. But this work is rather seasonal and highly volatile earnings. Besides, in the city where you live should be a place where local artists are exhibited. There usually is this part time job.
Another option is to open a workshop, in which you can do crafts: painted ceramics, wooden toys, production of Souvenirs, etc. you must register as an individual entrepreneur and to purchase the necessary equipment.
You can contact the employment center and wait for a suitable vacancy.