A lot of conpanies want a BA or BFA, but some will accept an associates in graphics design coupled with years of experience. And some companies will even forego the degree in lieu of tons of experience, so you need a portfolio any way that you go. I suggest formal training, because most schools will help you groom your portfolio as you go along.

You will need a combination of an education and a good portfolio. Graphic design is a very popular field these days, so there are quite a few designers working for or looking for work these days, so you have to find ways to make yourself standout.

The most obvious method, of course, is to get yourself a higher degree. A Bachelor's would be helpful, but a Master's would be even better. Believe it or not, there are even PhD programs being offered in design, though you likely won't need to take it that far.

A good portfolio is another requirement of the field. Your portfolio is your resume to the graphic design world, so you have to capture the attention of a potential employer almost immediately. How you choose to do this is up to you, but you have take a creative approach of doing it to make yourself stand out from the crowd.

As someone who has reviewed resumes and portfolios, I am often forced to eliminate candidates in arbitrary manners such as their education, whether or not they designed their resume, or the type of portfolio that they submitted for a position. It's a bit unfair, but it's necessary when you receive hundreds of resumes to fill one or two positions. How would you make yourself stand out from hundreds of resumes? That would be up to your creativity, education, and how you present yourself visually through your resume and portfolio.