From the NYT guide to Twitter, which reads like it was written for people who don't ever plan on using Twitter:
Once you’ve found people to follow, engage them. Send them a link to an interesting article. (To save character space when sending a link, use a Web address shortening service like Bit.ly.) Interact with them: respond to their tweets by hitting “reply,” mention the articles they share, show that you like a tweet by hitting the “favorite” button. When all else fails, try a compliment.
When all else fails? Aww, be a stalker and a sycophant!
You know how in the hit '80s caper film Top Gun, Tom Cruise (i.e., Maverick) is forever causing kerfuffles by chasing bogeys/going below the deck, and that one red-faced commander is always hollering "Do not engage! I repeat, do not engage!" because engagement = Soviet disaster or coffee spills?
That's how I feel about interacting with Twitter followers. It feels creepy to tweet at total strangers and I feel gross when I lamely attempt it, and it's even creepier when a total stranger tweets at me, like they just walked into my house, took off all their clothes and rolled around in my bed. I can't figure out how to scale this psycho-social hurdle, but it's really holding back my fameball dreams.*
* I have zero fameball dreams.
Found some Top Gun fan fiction, btw.**
** I did not read it.
Related: on Twitter verification (or not).