A large number of artists prefer to send a portfolio with some samples of their work rather than composing a resume, when as a matter of fact, many employers that hire artists are not always artists themselves so they may prefer to get applications in the traditional way. Learning to compose your own resume and a cover letter may not be a bad idea.
Let's start with the cover letter. Make it short and explain why you want to fit that position, be polite giving your reasons and add your qualifications, don't be exhaustive on this, just mention them. Finally, sign in and give your contact details.
Also describe your experience, if you are applying for a painter or illustrator job then you should have your portfolio online, so you can add a link to your own resume and make it easier for the employer to take a look at your job.
Herewith you will find very helpful resume samples: