This has sort of been covered by others but, try not to be tempted (as hard as it is) into a job (such as an artworker) if you want to be a designer. I made that mistake when I first started out and it took me a good three years then to build up a good design portfolio.
I was doing odds and ends of design and artwork at a small studio which was good experience but the quality of the briefs wasn't good enough.
I know now that I should have held out for a practice that I really wanted to work at.
My advice would be, take a look around the area where you want to work, then choose somewhere that's doing work you would like to do then home in on them. Find out everything about them, work they've done. work they're doing, people's names, awards they've won, are they on Facebook, twitter and all that old bollocks, get involved,contact the creative director - offer to go in and make tea for a week, take a job they've done and if you think you're good enough, show what you'd done, do one every week and send it in...even better, if you can take it in, get to know the person (probably Girl) on the desk, build up a relationship so the jobs eventually don't go in the bin.
It's much easier to concentrate on one target and because if you are tenacious enough something will happen - the worst is they'll tell you to clear off and leave them alone - you then use all you've learned and choose someone else.