I just started using Twitter not that long ago, but I am very happy with the results.
1. I suggest using tweetdeck to help organize your social networks. It will also automatically shorten your links and tweets and set up columns for your searches.
2. Search keywords that are important to you (you can use hashtags # to look for tweets tagged by authors) (i.e. #edtech #edchat)
3. Once you find a tweet that really interests you, check out the author. I always look to make sure they don't include too many personal tweets and that several of their most recent tweets are of interest to me.
4. As you build your network, you will notice lots of retweets (RT). You can continue to build your network by checking out the original authors of those tweets.