Twitter is still a relatively new social networking site and using it can be an art form all of its own. It is totally unlike anything you will do anywhere else.
Twitter allows you to add url links in your twits (you will need to restrain yourself from getting carried away and posting links too often.) The short length of the messages (140 characters) you are allowed to send means that you have to approach the task in a completely different way. It takes a bit of work and a bit of thought to use Twitter effectively.
Make sure that your twits are of value and are interesting. If you can keep abreast of breaking news, and the latest trends in your area of expertise, you can build up a reputation as being someone to watch out for. This will keep you on people's friend lists, and give you the chance to broadcast an occasional message about your own website or profile which will encourage them to visit.
Since you are looking to build a long term business presence, you will need to take a long term view and work to build up your network of friends. These friends can see your twits on their twitter home page, so it is well worth making the effort to cultivate as many as you can.
As with just about any other social networking site you can mention, you have to put in the hard work at the start to establish yourself as a credible, helpful contributor who is there to do more than just give a sales message and win customers.
Driving social network traffic is never quick or easy, but you can build up a reputation which will result in regular visitors to your site, who have every chance of becoming regular customers.
You can follow me on twitter here: http://twitter.com/ejcooksey