When starting your career, make sure that you make your boss look good.
I can't agree with this enough. I realised this about the same time I became my own boss (about 15 years too late). In my early career if I'd been less of an arrogant shit who was more concerned with pointing out the flaws in my superiors and more concerned with improving on my own I'd have gone a _lot_ further than I did.
In my early years, I focused intensely on learning everything I possibly could. This just happened to make my boss look good, but that was a bi-product of my desire to learn how to solve any and all problems. During my on the clock hours, I focused on my job, and during off hours (approved by the boss), I would learn everyone else's jobs. It's not that I wanted to do their jobs, but ti was much easier to excel at my own job when I knew the big picture - what feeds my job and what my job feeds into. At that point, the boss was willing to share more big picture business concepts with me so I was able to understand the business as a whole. Shortly after, I left and started my own business (not competing of course) and never looked back.
Being a professional is a mindset. It is a mindset of seeking to be the best at what you do and do it with a pleasant attitude. It's not about having all the answers all the time, it's about knowing the right questions to ask and how to discover the answer. If you are an EE, the degree and book knowledge you get with that is merely the ticket that gets you in the door. As others have said, your job is to solve problems. To solve the problems, you have to able to know what the problem is and how to break it down into manageable chunks and then solve it. If you take the route I did and others have wrote about, you would have at least a solid working knowledge of peripheral fields - mechanical, management, IT, software, etc. I went a little overboard on that note and have a very broad skill set, that only goes so deep. I have been a contractor for over 20 years and so have a variety of experiences working from NASA/USA (Houston/KSC), Oil field, Medical, Manufacturing, Broadcasting, etc. I have seen first hand which people rise to the top and which ones are stuck.
Be pleasant.
Listen.
Make peace with the reality that you will never know all the answers.
Learn how to learn.
When it seems impossible, just wait a few minutes - solutions tend to arrive when you are are less focused on the problem.
Take the time to understand the perceptive of your peers. They may indeed be stupid, but you should let them prove it all by themselves.
Self-educate constantly. Read and explore the industry for information and new ideas. This will help at your current job or help you discover a better one.
Be a salesman - you have to sell the others on why they should jump on board with your idea instead the theirs.