I went from internship into full time position and this is my advice from my experience:
1. Align yourself with the right people : I quickly became friends with key people inside the org, and honestly I didn't do this on purpose but it really helped me. I found myself gravitating towards the people working really hard and most interested in pushing the company forward, and quickly found that in many organizations there is a small group of "change makers." One thing about this is that none of these people were in design. I tried to align myself and understand what was important to the heads of our engineering teams, R&D Director, marketing, and even sales.
2. The classic "Come in early, stay late": This is important, but don't confuse it with "Wow he comes in early and leaves late, hes such a hard worker." I know so many people who implement this tactic, yet get less work done than some of us who work closer to 40 on average. I will admit, I often work more than 40, but I do try to keep a balance between work and life and the right employers will understand this importance. With that said, if I have to work over 40, its usually because I am making that choice because it needs to be done, not because i'm being asked. Dedication matters, especially if you're a millennial, everyone thinks we are flakes
3. Don't require a babysitter : Collect your mentors, listen to your boss, but don't require them to constantly micro-manage you (unless they do that naturally, which is a whole different conversation).
4. Get lots of sleep and work hard: Some people don't need a good nights sleep, but it helps me a TON and definitely impacted my good work while being an intern. I know school can make this difficult sometimes, but try your best while at school to just push through the day and utilize every minute possible to get work done. It will be tiring, but the sleep will be worth it.