I know a few people in this field and my biggest advice is start making a portfolio. Start animating! You'll want to collect your works so that when a prospective employer is interested in you, you can show them what you're capable of animating. The other thing too about working on your portfolio is improving your skills as an animator. This isn't limited to just your drawing and/or animating skills, but also learning the technology used in the industry. For instance, if you wanted to work on 3D animation like Pixar, look into some of the software they may be using. For this, look into Blender as it's 100% free to use.
Just know that animating is a very competitive field. Like you, many people want to work doing what they love. I'm not saying this to discourage you, just know that if you want to make this happen you'll need to give your best!
One thing that most people fail to understand is that there are hundreds of people in the arts that help in producing TV and Movies. What you want to do is figure out if you want to work on TV shows or Movies? (There time line for production are different and how they tell overall stories). Once you figure this out next you want to research about pre production, production, and post. These categories of production have different artist working in them. Since you said a famous cartoonist you might want to work in pre-production designing the world, characters and background the animators will bring to life in production! Once you have general idea of the type of artist you want to be, look up professional that are that type of artist from productions companies you like or shows you watch so you can get a sense of there portfolio.
Portfolios are very important in this career so it helps to research others portfolios to understand how to produce final art pieces to fit into the type of art portfolio you want to design. Also practice everyday on your art along with learning the fundamentals, like color theory and perspective. Do not think you have to go to traditional schooling for this career either, many people learn through online programs instead of in fine art colleges. It all about how you learn. Of course in does not hurt to work in adobe art programs(photoshop etc.) to build technical skills or in Maya for 3D animation.
Now if it Animation you want to do then that a different approach(portfolios still count) since there different animators for different things such as a rigger to move the character or 3-D molder. If you like to reach out for more information I would like to provide more, but research more first.
Step 1: Cartoonists usually earn a Bachelor degree in art and design or fine arts that includes courses in drawing skills and storytelling techniques. Courses may include cartoon history, experimental and narrative storytelling, inking and illustration. Apply for an internship with a professional cartoonist, while working on your portfolio.
Step 2: Choose a cartooning genre (politics, humor, etc.)
Step 3: Build Your Portfolio
Step 4: Publicize Your Work
Step 5: Find Cartoon Art Jobs