Well first a larger company is likely to distinguish between a 'designer', a 'developer', and a 'programmer' and sometimes in other ways. Sure every member of the team has skills that cross areas, but when working with companies that are large enough to have a web department, its often the case they want people who specialize a little in one area or another. Some smaller businesses have just a tech guy to do everything, probably also related to hardware and so on.
I think to get a job you should be familiar with these concepts
- Creating valid markup
- Working with the code directly and understanding browser nuances
- At least a working understanding of some programming language beyond html/css
Some companies won't know what this means, but many are starting to wake up. They know that web design is evolving from its roots, so you need to be up to speed at least enough to convince them you can keep up.
If you want to do graphics, I think that is a lot harder to break into without more experience. If you want to do coding, it sounds like you are more along those lines, then it might be a little easier since often code works or doesn't work, where as graphics have to have a certain appeal. I don't think you are a programmer, so I don't suggest going after one of those spots.
Here is what I'd do. If you are serious about going after a (good) job in web development, then you should first make a portfolio. If you need some sites, then find some non-for-profits to volunteer for. It sounds like you want to work for a company, so you need to look at some job ads and see what they want. Usually they list a lot of stuff, and its not normal for one person to be perfect at all of the skills. It does show you a list of things you should at least be familiar with and competent enough to use at least a little bit.
Otherwise, you just have to try. I've never worked at a company, but I freelance. So my experience is a little from the outside, but I've worked with dev teams and this is my understanding of them (at least of larger ones).
jeremy - gnomeontherun
Educated questions often get educated answers, and simple questions often get simple answers.