Using Twitter and Facebook to create strong relationships with people you've never met is much more challenging than people realize. (LinkedIn is easier because it stays on professional topic 90% of the time.) I once offended someone I really admire by trying to be funny on Twitter. Two years later, I still wince when I think about it, and she offered me no opportunity to apologize... just decided I was a troll. Fortunately, she didn't share her opinion with anyone else (that I can tell).
Mark Suster has published an excellent list of tips on Inc., linked below, although I don't agree about trying to be funny on Twitter anymore.
On thing that he doesn't mention is the importance of sharing the good stuff you see. Someone who's working hard to increase their influence deeply appreciates it when you share their work, especially if you add a compliment.
Inc.: How to Build Online Relationships Into Meaningful Networks, 2015-Jan-26 by Mark Suster
Figuring out how to engage is tricky. You want to be respectful. You want to say something informed. You want to toe the line between friendly public comment and being smothering.