It has been a great many years since I was fresh out of school. I now own my own company and employ nearly 50 people.
The way I got to live the dream is by being honest and having integrity from the get go. That means saying what is on your mind, professionally and personally, and above all, being NICE about it. Also, being flexible and eager to go outside my comfort zone was a huge help in learning everything I had to learn to go out on my own. The biggest mistakes I see "green" engineers make are:
1) Getting defensive. You're going to be wrong. A lot. You have a lot to learn, and a winning attitude is to accept this and seek out learning opportunities. There are certain school I just won't hire from anymore because they program their students with ultra large egos, probably to compensate for the ultra large price of tuition. There isn't much room for ego in an Associate Engineer position.
2) Getting lazy. We all realize you've been busting your ass to get your degree, and that being a good student is more than a full time job. But, you don't get to stop working hard just because you graduate.
3) Closely related to being lazy is: doing the bare minimum. You'll likely not be assigned enough work to keep you busy for 40 hours, but it will generally be expected that you spend the remaining time seeking out learning opportunities, reaching out to people for new work, and generally being eager and inquisitive.
4) Pigeon-holing: I see this one a lot too. Having your first real job is scary, and often I've seen new grads learn their first new skill, get comfortable with it, and then not want to do anything else. I would say the first 10 years of your career are not the time to specialize in something. The first 10 years are for exploring different skills and use cases and finding out what you're really good at.
I think the top three things you can do during the first year in your new job are:
1) Get to know everyone you can and what they do, and learn something about it, and how it ties in to the overall goals of the company
2) Be helpful. Offer to assist more senior engineers with testing, documentation, or whatever. You need to learn how to do the mundane and seniors will definitely appreciate your help in doing some of those tasks.
3) SAY SOMETHING when you get into trouble. If you're getting behind, don't know how to do something, or need help, SAY IT. You will not get in trouble for not knowing what to do, and the only way to learn is to ask. "I don't know" is not an obscene phrase.