Rookie Tip: Don't try to "prove yourself." Try to be effective. - Archinect

Often times, early in our careers, we ruminate over questions tied to a desire to prove our worth to an employer. “I need to show them that they made the right choice in hiring me,” or “I can’t ask too many questions or they’ll think I’m stupid.” Whatever it is, when we focus so much on ourselves we end up inadvertently doing a worse job because we are preoccupied with our insecurity rather than with performing well.

Instead, we would do better to realize that our goal is to make the lives of those around us easier. Do not worry about getting recognition, let the person directly above you have all of the recognition, make them look good, make their life exponentially easier than it was before you arrived. This should be the primary focus.

Go the effective extra mile

Consider this example: I used to always try to anticipate what my supervisor may not have thought of for a meeting, it could have been something small like tracing paper, an extra pen, a print out of an email. Anything that could have had the possibility of coming up, I wanted to be the guy who had it ready to go.

Take it a step further: say I needed help with some aspect of the building code. Instead of merely bringing the code book to my mentor, I'd print out the specific section in question and highlight the portions I was going to ask about, then l'd print out (or bookmark) any sections that the section in my query referred to and highlight the relevant sections in those also. I'd then make sure the sheets were ordered in a way that followed the flow of how I would ask my question and then, after having prepared this, I'd go and ask.

Seek to engineer ease

The goal was to make the interaction the simplest and easiest process for the person I was going to talk to. Most of the time it was something that took maybe a minute or so to answer, but I like to think that if I didn’t prepare everything in this way that it would have taken longer. It might seem nit-picky and unnecessary, but taking extra steps not only diminishes the work for those around you (my mentor did not have to go find the code book in the library, search for all of the sections for me, and then read them to try and make connections), it also increases your ability to investigate the problems that you will inevitably face.

Be the one that makes the lives of others easier and more convenient and you will naturally do what you were so concerned about before; you will prove yourself. This isn't brown nosing or kissing a bunch of ass. Imagine someone like the Chief of Staff to the President, he or she is not a kiss ass, but rather an indispensable ally. As one learns more and becomes more indispensable, they soon find themselves positions of higher responsibility, that eventually lead to a reversal of these roles. In the end, it is only a matter of time.