Do you mean follower or visitor? In twitter you need to follow first so that you cant get followers. Or maybe I am not really expert on twitter. How can they visit? They should have their own twitter account.
ya have to increase your follower than you post you link or information about your site then your go the number of visitor
After you join twitter, folow people from your niche and they will most prob follow you back - send out good tweets often - When you have a reasonable number of followers, show off your follower count in your site using twittercounter and you will get even more followers and so more people to click on the links you post to your twitter and more traffic.
It all depends who you are targeting and what your goals are. If you want to create awareness and "buzz" around your brand or products then the prize give away is a good way to go. It's a very simply, low cost and time efficient way of effectively utilising twitter. If consumers are not your target and you are looking to attract businesses and their key decision makers then there is no fast route to success. This can only be achieved by engaging with the community, both through twitter directly and on other relevant social sites, requiring a far greater investment in terms of time and commitment. I'm currently running my own little experiment to see if I can get 10,000 followers on twitter inside of 30 days. Anyone think it's possible? Would love to get your feedback! ps. my twitter ID is "christelferuk"...add me!