I started by hearing about it on Etsy, 1 of 2 handmade sites I sell on. At first, I pretty much listed links to new items for sale, a plus if you want your items to get views. We also spend a lot of time cheering each other on when sales are made.
But, as I started following more people, total strangers started following me. I customarily read their bio and check out any links they have. If they sound interesting, I follow back. And these people started listing links to all kinds of things that range from quirky, to serious, to hysterically funny, to political. As you reply back (easy to do by hitting a funky arrow button next to their post) you can often find yourself flooded with their followers suddenly following you.
As a WAHM, my socializing is limited to the 15 minutes I go early & hang out with other kindergarten moms as we pick up our kids at school, so Twitter has become my link with the outside world. Snowstorms on the East coast, I'm playing devil's advocate & posting my 75 degree weather. Breaking news from the reporter in Chicago, I'm waiting for the updated posts. There's even a novel in progress that comes in batches of 5 tweets at a time. A pretty big challenge considering you're limited to 140 characters per post.
So if you haven't Tweeted, give it a try. You can click on my link at the bottom and read some of my posts (although, they may seem pretty boring). You can then click on the names of anyone I've replied to and see what they have to say. Once you start following the threads, you'll be well on your way to being addicted too. I warned you!