Make an impressive portfolio of sample works. If you have no prior professional experience to include in your portfolio, you can still make sample storyboards for a variety of subjects such as film, TV commercials or advertising. You can also showcase storyboard projects you had in school, if any. You could even re-create a popular movie's storyboard. Potential employers place more weight on submitted visual materials than on a written resume. However, including a resume in a typical application is still necessary.
Accept all work, even small commissioned works or pro bono projects, to help you build your samples and portfolio. These jobs also allow you to gain more experience in the industry and acquire more contacts for future projects.
Package your portfolio, sample works, resume and cover letter together using a creative concept, for example making them work together as one whole artwork. Since you are trying to get into a creative industry, aesthetics matter. The keys to being remembered are visual appeal and making a striking statement through your artwork and your application. You may also submit traditional application documents if you are confident that they would work better. Remember that each production company that can hire you has its own tastes and preferences.
Create an online portfolio, preferably using your own domain name and website. An online presence adds to your credibility. Add links to your other online profiles and sample works on sites such as LinkedIn, deviantART, Facebook, Youtube and Vimeo.
Make a business card and always have copies handy for potential clients when you incidentally meet them at conventions, meetings, conferences and parties. The card should list links to your website or online portfolio.
Look for prospective storyboard artist jobs online or through friends, colleagues and other network sources. Check for openings in job sites and the specific websites of companies you want to work with, such as film, animation, advertising and gaming studios.