How can one become a graphic designer?

The best one is Adobe... The whole Adobe Suite is the best. But it's a little expensive. I first started graphic designing on Microsoft Publisher, which is pretty easy to use if you're just starting...

Edit: More information on Adobe Programs:

Adobe InDesign: This program is absolutely necessary for creating type layouts for magazine pages and spreads, flyers, brochures, or anything that has a large amount of text.

Photoshop

Adobe Illustrator: Necessary for creating vector graphics, which will be paramount for designers creating logos and illustrations that need to be sharp and hold their quality whenever re-sized.

Adobe Photoshop: Necessary for creating raster graphics and editing Photography.

You can also use Adobe Dreamweaver and Flash for creating web pages and animation.

You may also find some companies asking for experience in Quark Xpress. This program pretty much operates similarly to Adobe InDesign as they're both used for layouts.

Also, if you are a student you should be able to purchase Adobe programs with a Student/Teacher license for a relatively affordable price. However, there are certain restrictions that come with an educational license that you can find more information about on the Adobe website.