How should someone start off their graphic design career?

I would start by taking as many art classes as you can. Drawing, painting, pottery, photography- whatever works for you. These will give you a great background in the principles of design that will serve you well as you move into graphic design. Work on learning how to use Adobe Creative Suite software if you haven't already. Get a student account and work on some projects, get really familiar with the ins and outs of Photoshop, Illustrator, InDesign, After Effects etc.

Alongside that- many graphic designers wind up working for corporations, in marketing departments or otherwise, at some point. Take a few business courses, and maybe a business or technical writing course- designers who are also great writers and business people go a long long way.

Look into graphic design programs- depending on where you want to go to school, you might be looking at different levels of technical focus- decide what is most important to you and pursue those programs! Ensure that wherever you go, that you'll come out of the program with a well-developed portfolio. It's a great tool to get you hired in your first position out of school.

Good luck!

Carry a camera and take photos of things you like.

Have a sketchpad for notes, dreams, sketches and doodles. Maybe set yourself a daily creative project, like sketching strangers on the train.

Use Adobe's Photoshop & Illustrator etc - understand the difference between bitmap and vector graphics.
Dive in and try all the tools out there, but remember some are used professionally and some are not.

Learn about how humans see. Gestalt psycology on Wikipedia

Learn about typography. The documentary about Helvetica is worth a watch.
Maybe try designing a typeface Fontstruct

I have often learnt from watching how others approach creative problem solving - never be afraid to ask!

Become a design geek...

Good luck!

My degree is in graphic design and studio arts. I went to school 4 years in Nebraska, but now there are lots of schools that offer this as a program. Check into getting your BFA or BA. I have a BA. I would become familiar with as many art and figure classes as possible. You can do lots from greeting card design to online programming with your skills. I took classes in photography, pottery, portfolio design, resume writing, lots of figure and studio classes, graphic design and illustration and more. Become well-versed in many artistic disciplines. My first art job out of school I worked at a church and layed out the bulletins and flyers. Know the type-setting rules for the time period. I would also take some basic writing classes to learn some basic skills. Offer to create logos for small startups. Combination marks are good to create - even if for a fake company to show your skills.

One good start is to find a school you are interested in and get a degree. But very importantly, something I did not do while in school, is to look for internships. The connections you make will be equally as important as the degree you earn.

There are ways to find a job without a degree though. Continuously search job sites for junior designer jobs. If you still need to learn the basics before jumping into a career, an internship is a great start. Check blogs, watch youtube videos, and try to network within the field. Once you have a grasp start doing freelance jobs or even unpaid projects to help you learn. The more you experiment and play with the programs (like adobe suite) the more you will develop the skill. Hope this helps!

I would say doing as many projects as possible. Even little ones for friends and acquaintances. Graphic design is many things to many people. There are icons, logos, brands, colors, marketing, advertising, interfaces among other things to consider working on. It is largely an interpretive skill. A good way to get started is to go to sites like dribbble.com to get some inspiration. Imitation is a good way to start. The big three applications designers use are Photoshop, InDesign, and Illustrator. However, there are up and coming applications called Sketch and Affinity that are newer and less the behemoths that people like me have been using for a while. A lot of young designers in the UI space are using Sketch. Building a portfolio is key. Essentially you will live or die through your portfolio. So building it up through logos, website design and print design is essential. For some of the applications I mentioned there's a lot of tutorials on YouTube you can do.