My input as one who has hired artist for games, cards and such.
The above is good advice and to add to it:
Be willing and able to take critizism of your work. Even if you believe the person knows nothing of what they talk about. It is a major turn off to an employer to have an artist get 'sensitive' over comments.
Show your work to others.
This means more than just your family and friends. Go to Comic, Game, Artist and other types of conventions where companies and artists will be at. Attend seminars and/or gatherings that other 'successful' artist put on. Some are free, and those are the ones that I would suggest first.
Don't worry if the artist giving the 'talk' is not of the type of artist you are working on becoming. If they are successful, are making money, and are known, there is a reason. Listen to them.
As you progress, be willing to get your own table at some of these shows. Make copies of some of your artwork for sale. Consider even selling some of your originals (Not required but ... This is a different topic on art and artist). I would say that about 1/3 of the artist that I ended up hiring or reccomending to be hired by my company I found at shows and conventions.
Once you find the type(s) of companies that you would like to work for, frequent the areas (conventions, forums, etc) that they have a presence on. From there you will get a feel for what they want, and sometimes the companies will place notices (not that common but it does happen).
Ask,
this means this thread was a good start. And once you have some solid work (art and experience) built up, send a nice (professional) letter (email) to the company asking what their requirements are for artist (hiring, format, etc) and how you might be considered for any of their future art needs.
Sending them artwork is not always a good idea, (legal and other issues) but having a signature art piece that you use all the time or a website that they can look at is very helpful.
If you get a 'thank you but no thank reply', don't let that depress you. Most companies will reject 80% (or higher), the offers for work from artist.
If you get an invite from a company to look over your work, don't let it go to your head. Go to the meeting, be prepared to hear lots of good and bad and other about your art work, and ask questions. (there is some other advice but that is a different subject).
Don't be demanding. Unless you become like Larry Elmore (or some other big names) making demands will get a close door very fast.
Some well known artists started working for almost nothing doing pencil and pen drawing pieces for game companies even when they (the artist) were wanting to be color, full sized picture types.
And finally (for now
) if you are not one who is much for the business end of it, find someone (family, friends, artist groups, etc) whom you fully trust to assist you.
There are several artist groups out there and there are some good solo artists that could help you get started ro pointed in the right direction.
Hope this helps. It might be more than you need to know or deal with right this moment in your pursuit of being an artist but tuck it away for now and look it over later.
Dave Chase