It can be difficult to start using Twitter, since you must decide who to follow and it will take some time before people follow you back, let alone interact with you. Imagine yourself walking into a room full of interesting people, all having conversations with each other. Do you expect everyone to notice that you have arrived, stop what they’re doing, and greet you warmly? Or do you expect that you will need to find someone interesting and join their conversation?

The first thing you should do is locate a few interesting people to follow. Don’t go with the initial set that Twitter offers. Rather, think of some people (both famous and ordinary) that you would like to have a conversation with. Search for their Twitter people and follow them. Since you’re reading this, you might like to start with me (SFoskett) and some of the Tech Field Day delegates (my tfd-delegates list)!
After you have done this, Twitter will recommend other interesting people in the “who to follow” box. Don’t bother with anyone “Promoted” (that means they paid to be suggested) and focus on the “natural” suggestions. These will be people followed by, or similar to, the people you selected above.

Look through the “Tweets” of these people, and see who they interact with. Follow some of them as well. And check out who the people you respect are following (here’s my list) until you have followed a few dozen people.
Read what they have written, how they interact, then join the conversation. Reply to something they say or chime in with an interesting anecdote, and see what happens.
Many new twitter users wonder why no one pays attention to what they say, but there is a reason for this: Only people who follow you will see your simple tweets, and it is unlikely that many people are following a new user. Twitter users are not actively trying to exclude you, they just are not seeing what you are writing.
Join a conversation by including the “@TwitterID” of some people who will be interested in your tweet so they will see it. They may decide to follow you back, and begin conversing with you. I personally follow back anyone who engages in interesting conversation with me, and I believe many others do as well.
If you’re having trouble engaging with other Twitter users, consider the form and content of your tweets. Are they interesting, with wry observations and witty anecdotes? Are they readable, following convention for format and grammar? Are they directed at people who will care about the topic? And, once again, are you engaging people by including their @TwitterID so they will see what you’re saying?
It’s very easy to get dispirited at first. I actually created a test Twitter account to try these suggestions, and it took weeks before I had any real interaction and followers. I empathize with the plight of the new tweeter, but I heartily recommend that you stick with it. Once you’re part of the Twitter conversation, it’s worth it!