Graphic Design comes in two flavors – Web and Print.
Print design comes with its own rules and principles. Print typography is very different from web typography but you may see some cross over. Graphic Design of the print variety has a slightly different aesthetic but requires the same design eye, and ability to organize information.
Software you will need to know for print: Illustrator, In Design, Photoshop are a great start.
Web Design is a different beast. There are many web designers who do not know how to code, but they do understand the underlying fundamentals of user behavior and expected behavior. So for example having the login information at the upper right hand of the page is not required, but you would expect it to be there. If you surf the web a lot and look at many examples of sites you will get the gist of what a user is going to expect. Now take that and add a sprinkle of creativity and you’ve got web design.
Software you will need to know for web design is: Photoshop, Illustrator – maybe Dreamweaver and Adobe Muse. You may also want to learn some wire framing and prototyping software.