I'd recommend going to work for a mid-sized firm (5 or 6 licensed engineers) that will allow you work on a variety of projects involving wood, steel, masonry and concrete. ask if the engineers will let you go with them into the field to do site visits. you will learn as much about engineering by seeing things being constructed and hearing the contractors discuss issues as you will sitting in the office all day.
I agree with the statement that just because a senior engineer said so, doesn't make it so. but at the same time, beware of being disagreeable with them. I have two interns working for me. one of them argued with me about an issue because it didn't seem possible to him, but he had yet to experience the issue. "trust but verify... diplomatically." pick their brains, but don't distrust the older engineers.
ask lots of questions, but be thoughtful about what you ask. think about a solution, ask if you are on the right track with it instead of asking to take the easy way out. use judgement based on what you've learned from your mentors. during the first six months, you will likely be a pest with lots of questions. after one year, the type of questions should become more thoughtful and less frequent. if you are still asking the same type of questions after one year that you asked in the first six months, you may not be trying to become an engineer.
take some intitiative to help your company finish work as quickly as possible. it's not just a job. your firm sells service. if the service stinks, your firm has nothing to sell. the service is only as good as the people providing it, and you are one of those people. if you do a good job and are timely with finishing your work, your bosses will likely remember that. if you have two weeks to do a job and can finish in one week, do so. don't milk the project budget appearing to be busy. "kill it and bill it."
attend every AISC, ACI and structural engineering organization seminar or meeting you can possibly attend. especially the ones where it only costs you the price of lunch or dinner. if your boss offers to send you, go. don't be afraid to ask to attend a seminar, but don't be mad if the boss says no. AISC and ACI seminars are expensive. offer to split the costs or pay on your own. the amounts are tax deductible and you can learn alot early in your career.