If it is a blog then you should be able to use key words and content to drive the traffic. This does rely on you regularly updating your blog. Don’t forget to register your blog with the search engines and ping it. – All for free.
If you are using WordPress you can use a Plugin to have your new posts and/or updated posts sent to pingomatic automatically.
Another important step for getting traffic to your blog is sharing your new blog post on Twitter and Facebook. You can use Networked Blogs on Facebook with an RSS feed to have your posts fed to Facebook. If your blog is a business one and you also have a Fan Page, then you can have the Feed posted directly to your Fan Page. If your Facebook Page is linked to a Twitter account then a new Tweet will be automatically sent at the same time.
With Networked Blogs you can add a Widget to your blog to get followers. People can follow by visiting your blog or you can send invites to your friends to follow from within Facebook.
For a website with static content driving traffic to your site is not the same as with a blog. If you are selling a product and/or service then I recommend listing your business with as many free online directories as possible. Start with the top 5 for your country and continue to add another 5 a week. In the USA, Merchant Circle has been a great resource for us. If you want additional exposure you may want to look into upgrading to a paid service.
Another option is to set up reciprocal marketing with another blog or site owner. You put a link/ad on your website in exchange for your link on another. There are questions amongst Search Engine Optimization (SEO) experts as to whether this is a good strategy and whether two or three sites are required. Opinions on this topic will probably change from month to month so I recommend doing a little bit of research if you are concerned about potential negative impact to your search engine rankings.
Do you have additional suggestions or questions?