First up, what is Twitter? It's a social networking tool, for personal and business use. It's used for micro-blogging. You basically create an account and a user name and you can then start 'tweeting'. A 'tweet' is a message (which has a maximum of 140 characters) that you post to your twitter profile.
So, why use Twitter? It's a quick and easy way to say something publicly and connect with potential and existing customers.
You can use hashtags which make it easy to find people who are tweeting about similar topics that you are. Turn a word into a hashtag by adding the "#" sign before you use the word, e.g. "we've just completed an article on #Facebook"
Twitter's '@Mention' system enables you to contact any other Twitter user, by placing an "@" symbol in front of the Twitter user name in your tweet, e.g. "@facebook loving the new design"
If you like a tweet, you can retweet it to your own followers; this is one way that businesses can increase their following. If customers are tweeting/retweeting good things about your business, other people get to see this praise and may choose to follow you or check out your website.
What might you tweet about? For businesses, it's good to use Twitter to try to encourage people to visit your website, e.g. putting links to your site in your tweets. You could promote your industry, posting links to content that would be useful for your customers. Twitter is a good forum for advertising special offers and promotions that you may be running.
For more pointers and ideas on what you can tweet about, see http://www.chrisbrogan.com/50-ideas-on-using-twitter-for-business/
See http://business.twitter.com to get you started.
Twitter is relatively quick and easy to use and is a great way to keep your website updated. You can organise your Twitter updates to appear on your Facebook page-kill two birds with one stone!