Promoting your website with articles on other websites has become the most popular way to gain visitors to your own site..
Write an article about your website at least 500 words long. Don't promote a product or service, just write about something other people want to learn about. Go to www.ezinearticles.com to see what I mean. Read a few articles from other people to see how to write your own.
Once you write the article you'll have to create an account on the article website so that you can add articles. Then you'll add the article, add a title and keywords about the article and a Bio. The Bio section is where you want to add a link to your website. You're allowed to write a brief description of your company and website along with a link pointing to it in that section.
Creating Visits is a web design company based in NH that will create a website with guaranteed visitors!
You won't have a "link button" on this website, I don't think, so you have to surround the phrase you want linked with this code in the Bio section: <a href="Full URL here">Phrase Here</a> Make sure you preview the article before you publish it and the link should look like mine in the example above or you've done something wrong.
Continue to add articles because Ezine Articles is a huge website already, so when you add a page to their site with your link it will show up in the search engine right away to be viewed. Then you can check to see how many people clicked your Bio link and went to your website from there. When people like an article they will also copy it (with your link) and add it to their website which means you get another link from another website.
Search engines weigh a lot of results on the amount of links you have on other websites because they're so hard to get. People have to do it on their own by copying the article and adding it to their website which is usually unlikely but it happens. It's the beginning stages of promoting your website and making it more popular. It doesn't "just happen".
Social Media websites are also incredibly popular for promoting your website because people are on them non stop! If you have Facebook you should add a few wall posts about your new website and if your friends like it they will also write it on their wall to promote you. Then start using Twitter, Myspace, Youtube and much more...