How to become the first among equals
First remember that too many questions is better than too few. If you are afraid that your superior doesn't like questions from her employees, bear in mind that she certainly doesn't like an employee who has nothing to ask and is stuck in his cubicle.
That's especially true if you are new in the company: questions will show your coworkers and superior manager that you are genuinely interested in task at hand and that you want more than just doing your job and going home at 5pm. Of course, with time you won't be asking a question every few minutes but don't fall into "my job is to work and be quiet"; that's not good for your career.
Think about business process improvement. Is there something you can do easier, faster or with less resources? Is there a new procedure that company should adopt to improve the productivity or reduce cost? Is there any knowledge you could share with your coworkers? If you have something like that in mind - come forward.
Talk to your boss, share your knowledge and explain why life would be easier with your solution. Be prepared to hit the wall at first because it's hard to break a working routine, especially if your ideas are radically different, but bring arguments to the table and share your ideas with your boss.
If there's any education program that could improve your knowledge and productivity, don't be afraid to tell your superior manager about it and ask is there any chance for the company to send you to that education. No matter who's paying, you or your company, every managers likes an employee who is constantly trying to learn something new, something that can benefit both him and his company. If there's no immediate benefit, don't worry, the time will come for you to use what you have learned.
Listen what your coworkers have to say. Don't just push your ideas, listen and try to help others to bring their ideas to life. The goal here is to show that you care for other employees and for the whole company, and that you can be a team player. Even if you love to work alone, and let's face it - there are lone wolves out there, find the time to ask your colleagues do they need help and what can you do for them. Small favors can look small to you but as big as a mountain to others.
Go that extra mile. Let's say you have eight hours for your job and you're done in five. The biggest mistake you can make is to work slower just to fill those eight hours with something. If you are done earlier, tell that to your boss.
Companies have different rules for that situation: in some you'll be free to go home, in others you'll have to work half of the spared time for the company and the other half is yours. If there are no rules in your company, ask what should be done next. Again, that will show you that you thinking about your company, not just about yourself.
And remember the worst thing you can do: come at 9am, do your job, and leave at 5pm. If you are not helping others, if you show no intent to learn and have nothing to share with your boss, there's no reason for you to be promoted. ■