Think of twitter as a big cocktail party - everyone hanging out, shooting the breeze. So you kind of wander about, looking for interesting conversations to join, interesting people to meet. Sometimes it's "friend of a friend" like RC said. Sometimes it's a random stranger with a common interest that you bump into at the appetizer table when you both reach for the stuffed mushroom caps. Sometimes it's a random stranger who compliments you on your shoes (or vice versa).
I'm a huge introvert and pretty shy, actually but Twitter has been great for me because it's so easy to start a conversation, just respond to the things people say or join a conversation or join a twitter chat. There's a million ways to do it.
As a writer, you also should be working on connecting with FANS/READERS, not just other writers and industry professionals (though those are very important, too). Twitter is great for connecting with book bloggers, learning about the reader side of the biz (how NOT to promo a book, how NOT to respond to negative reviews, how TO run a successful giveaway, etc.), and learning great blogging tips (how to keep your blog interesting), finding things you can join to drive traffic to your website (like blog hops and such), etc. I've also used twitter to ask questions/get advice and to get referrals for help (most notably I asked for help finding a joomla saavy website developer and got connected to someone).
Hope this helps!