Getting started http://twitter.com/ - Be sure to upload a photo or logo to your account. Unless you are a company I highly suggest using a photo of yourself. Twitter is about relationships and noticed I feel more trusting when I can see a persons face. Also fill out the profile. When someone follows me but has nothing on their profile I rarely follow them back. And I suggest making a custom background that has some content you want people to be aware of.
GET A DESKTOP APPLICATION. You have filtering controls that make it much easier to use twitter. I prefer Tweetbot. It makes it easy to reply, direct message and read the tweets of those you are following.
Build a network. “Following” someone is the same thing as adding them as a Facebook friend, except that they dont see your updates unless they choose to follow you as well. You can go to http://search.twitter.com/advanced and search for your interests or do so right from Tweetdeck. When I find someone that I like I look and see who they are following and who is following them. Another source is http://monitter.com/. This site lets you monitor people by hashtags which denote groupings of twitter for popular commonly referenced items. For instance I use this hashtag to find iPhone photographers - #iphoneographers.
In general if the person has more people following them then they are following they may be worth following. I have found that without too much effort I have a group of people that I follow that I wouldn’t have connections with by other means. Twitter is like a relationship and like a relationship it takes work. If you want to be “heard” you need to “listen” and retweet valuable information.
If you want to be retweeted don’t use up all 140 characters. Leave enough space for people to retweet you without editing what you posted. I keep my posts to under 120 characters. Also, if your tweet starts with someone’s @username, only that user and folks who follow both of you can will see the tweet in their timeline.
ManageFlitter is a great way to see who you are following but isnt following you.
Its also a good idea to make links from your website and blogs to twitter. By posting on twitter the traffic has increased to my site and blog with an increase in sales.
There are lots of apps for phones and my favorite one for the iPhone is Tweetbot