Web Producer Education and Experience
Web producers create and manage the content for Web sites. The best Web producers have a strong understanding of marketing and PR and can write really well. Companies often hire Web producers who work well with other people, as they often act as the intermediaries between Web designers, programmers, and the rest of the company.
Web producers should have some type of liberal arts degree - what isn't as important as the fact that you got through a program with a lot of writing requirements. A marketing or PR degree wouldn't hurt, but often you'll be asked to focus more on Marketing and less on Web development if that's your focus.
Web production jobs often have the most diverse of titles. You might be a Web content owner, Web editor, Web writer, Web setter, copy writer, or something completely different. If you've got good writing skills and don't feel up to getting a degree in programming or design, this can be a great entry into the Web development field.
Gaining Web Development Experience
Remember that no one starts out being handed a completely blank slate and told "here is $1 million dollars to build our Web site". Everyone starts at the bottom. And the bottom for Web development can be really boring - maintenance.
If you've only built sites for your friends and family, you can still get a job at a company building Web sites - but chances are it will be a very junior level position. This is where everyone starts. Use this time fixing links and correcting typos to learn as much as you can. Every designer and programmer for a Web site is different, and if you try you can learn something from all of them.
Don't be afraid to suggest changes and design solutions - even if you are junior on the team. If your ideas are accepted, use them in your portfolio. If they aren't, save them in your design ideas folder and try to find out why it was rejected. Then use those criticisms to improve your next design or program. Every time you open up Dreamweaver to edit a Web page, think of it as an opportunity to learn more and improve your skills.