With animation, cartooning, and comic drawing you are going to probably want the following:
1. A strong portfolio that shows you can:
a. Draw things correctly in perspective, proportion, and with adaquate detail. I cannot stress enough how an accurate and realistic (in that it looks like a believable space) background ends up solidifying everything else in the drawing.
b. Draw people with simplified lines and forms.
c. Draw the same people over and over and over quickly and efficiently with a myriad of poses and expressions.
d. Compose images and figures such that they are interesting and dynamic.
e. If you are interested in colouring and inking, you'll want to show you can do that reasonably well, too.
2. A website. Doesn't have to be super-freakin awesome. Just make it clean, navigable, professional, and with an easy-to-remember domain name.
3. Go to conventions. Sell some of your artwork and/or talk to some of the art directors there. I have been told that others have found work by making something like a postcard that has a little bit of your artwork on it and your website/contact info. The point is to start networking (I hate this word) with people in the field.
4. Find other people who want to do/are doing the same things you're doing. Get to know them. Help each other. There are websites and forums where people post things... conceptart.org is one of these, though it might not be what you're looking for specifically. It will give you an idea, though.
5. Learn how to make submission packets. Information for how to do these is different for every company and they usually have guidelines for how to send in artwork.
Comic Book Company Addresses this website has a nice list of companies.
List of animation studios
6. You will need a standby job until you get rolling.
7. You could try starting a webcomic. This seems to be the way a lot of cartooning and comic strips are moving lately. Warning. Your comic will probably suck at first, but then it'll eventually get better.
8. Take a business class or five somewhere. Learn about different contracts and how to manage your own business. Even if you don't end up freelancing, this is
invaluable information! Learn everything you can about legal stuff. If you decide to freelance, learn about marketing and advertising. If you decide to freelance, don't quit your day job until you are sure you can make as much money freelancing as you do at your day job.
9. Be amicable.
That's about all I can think of that I've sort of gathered from others. It, like all things, takes time. Remember that
no one is going to come and sweep you off your feet and give you that magic job. You're going to have to work your ass off to get it or make it yourself.
Having said all that, don't let yourself be daunted by the details. You can do it. Just take nice, small steps.