Write fresh good quality articles and circulate them. Google bum marketing. It's the most inexpensive way to market. It's effective of done right.
Things you can do for free: write articles and upload to article directories with your link, make a youtube video with a link in description, manually trying to gain followers on twitter is also free, messaging people on facebook is also free, creating free blogger accounts that link to your site is also free. Most things can done for free, but of course paying for tools or outsourcing will automate the process and save time, but you can do most needed things for free.
If you are selling a product/service, use mostly free advertising, and before you use any paid advertising test on a small scale first before spending more. You can earn some extra income with freelancing, product reviews etc, by joining some free to join sites without paying anything upfront.
Marketing your website need not cost anything. You will just need to do everything on your own and be patient and committed in building links and promoting your site. You can write your own articles and post that in your site and submit some to article directories. Participate in blogs and forums within your niche to actively promote your site. Hope that helps. Have a good day!
If you want to learn how to market on a budget. You can do free marketing methods like social media, video marketing, forums, article marketing etc. Also there is a product called "Building Your Business On A Budget" by Mike Dillard. Its a very good resource if you have a limited budget.
Consider these ways: 1) free ads on classifieds (they are free) 2) free articles 3) submit free videos on video-networks They are free and they work!
Article Marketing, Directory Submissions, Forum and Blog Commenting, Social Media (twitter, digg, stumbleupon etc). There are MANY ways to market a website without spending a dime. It takes time because you can't afford automated tools, but it works.