Social media is one of the most used and best inexpensive ways to promote a website. Not only do you reach a lot of people to view the site or share content, you are also building up your website ranking by utilizing higher ranked sites (Facebook, Twitter, LinkedIn etc.). The better the ranking the higher your website will appear in search engines.
PPC advertising via social media can be customized to your budget as well and can target a very specific market.
Creating a blog within your site can bring organic traffic to your site by giving users relevant content and becoming a reliable source.
Adwords can be a great advertising resource, but this can get higher on the price scale depending on what your site is all about. (you are going to have to pay more for popular keywords)
Include your website in your email signature.
Email marketing is now very reasonable and can reach a lot of people in their most used form of communication. Sites like Icontact or Constant Contact offer plans that are very affordable. Include links to your main site, give teasers to articles and blog posts but most importantly give people useful information, not just a sales pitch.