Draw constantly. Draw at every opportunity, and draw a wide variety of subjects in a wide variety of skills to build more versatility as an artist.
Enroll in an animation program. Take a comprehensive program that offers a wide array of subjects and topics related to animation. A quick course that only lasts a few weeks and trains you in a very narrow portion of the industry doesn't prepare you well for work in the real world. Also, look for a school that includes building a demo as part of your program. For instance, the Art Institute schools offer a full bachelor's degree in animation. The Academy of Art University in San Francisco has both a bachelor's and master's degree in the field that provide comprehensive and advanced training.
Build a demo reel. A resume, especially one that only includes school-related experience, won't get you a job in the animation field. Accumulate your best samples to build a portfolio and a reel to submit when you apply for jobs.
Create your own work. The more you work on independent projects and create actual samples, the more prospective employers will find when researching you as a prospective hire. The Internet provides the perfect platform for independent animators to create samples of their work and to build an audience even before they get their first job.
Apply for internships. Some larger studios have internship opportunities that serve as great professional development opportunities for animators. Disney, for example, has an intern program that it calls the Associate Program that provides professional development to budding animators.
Apply with your resume, reel and portfolio to any and all jobs you find. Even if your goal is cartoons or feature-length animation, apply for all animation jobs when just starting out. Any experience in the industry will make you more employable.