When connecting with people on social media think about what similarities you have or what you could learn form this person. Then send them an email or a little note about how you are interested in their work or learning about what they do. This will go such a long way and won't be artificial, like the blank friend request the girl next to you just sent.
Invest in the coffee meet-up. Ask people who you are genuinely interested in to meet up for coffee. When you get there have questions or conversation topic prepared. An awkward business date is worse than an awkward boy-date. (Trust me) Then followup after the meetup with a thank you and elude to future correspondence.
Networking, well effective networking is really all about building relationships. (Which is also a huge part in PR, hurrah!) You want to formulate a bond with people, generate interest in yourself, so maybe when you need an internship or even a job you have people to contact and who knows maybe you could even help them out in some way!
Enjoy your coffee & LinkedIn addictions. xoxo