Recommend a New Intern: If you decide to leave your current internship and are still on good terms with your supervisors, recommend someone for your position. Make sure to speak to that person first and confirm they are interested in the role. Also, be confident that this person would be a good fit for the company.
Volunteer: Many professionals volunteer outside of the workplace, and may need help with an event they are participating in. If you have the time and are willing to commit, grab a couple of friends to volunteer at the event with!
Offer to Teach a Skill: As millennials we tend to pick up on trends a little faster. If your boss is older or there is someone else in the office who doesn't get an Excel shortcut or how to use Twitter, offer to help. Be careful not to sound superior, instead offer in a genuine way to help.
Send Articles: Send articles to them about their favorite sports team or a hobby you know they have. They'll appreciate the reading material and the fact that you remembered facts about them. Do it once or twice a week, but not more than that.
Networking is about building relationships with people you have a connection with, and having a mutually beneficial relationship. It's not about schmoozing and asking for something all the time.
Relax and be yourself! Don't worry!