Yes, experience is very important because it enable you to predict the situation coming up with your project. An engineer also need to be strong technically. Pay a very good attention at university! Moreover, an engineer has to have good communication skills. He has to be able to share his solutions/plans with other engineers and upper management.
This is a very broad question, but becoming a good engineer is all about getting experience. To do that you must be willing to spend extra time in learning things on your own as well as using those that have more experience around you to help you gain an understanding of things that take time to understand.
So it's really 2 things, experience, and while trying to gain that experience the desire and drive to learn on your own.
In addition to the great responses provided so far, I will add a bit more, specifically in the area of communication skills. It is very important for an engineer to have good communication skills. I emphasize this because engineers have a reputation of not being able to communicate well. The impact of that perception (or reality) would mean that someone who has designed something that could be potentially great, would lose that opportunity if others don't understand what the design is, how to use it or it's impact.
Even within having good communication skills, a good engineer is an excellent listener. Arguably, this is an important trait for any type of job :)...but particularly for an engineer who builds things/writes code/directs projects, having good listening skills is key to having successful outcomes...and it too, is something that comes with practice.
Best of luck to you!
Congratulations on being interested in becoming an engineer. Engineering is a very broad, interesting, and rewarding field. Here are some helpful sites for you to visit:
Best of luck. I would like to follow your progress! Please keep me posted.