Write articles that are themed along with the niche of your site. Write something that you have expertise on so that when they read it, they can feel your knowledge about the subject and will be eager to go to your site. Write articles that produce tips and guidelines to the subject or niche your site has.
Include a resource box at the end of your article that can link them to your site. Write a little about yourself and your site. If you provide a light, information-laden and interesting article, they will go to your site for more.
Make a Newsletter
This may sound like hard work because of all the articles you may need to use to build a newsletter but on the contrary, this is not so. There are many writers and sites that are willing to provide free articles as long as they can get their name in on your newsletter. This will also provide free advertising for them as well.
As your newsletter gets pass around, you can widen your public awareness and build an opt-in list that can regularly visit your site.
Join Online Communities and Forums
This only requires your time and nothing else. You can share your knowledge and expertise with many online communities as well as your website. You can get free advertising when you go to forums that have the same subject or niche with your site.
Share your two cents and let them see how knowledgeable you are with the subject. As you build your reputation, you also build the reputation of your site, making it a reputable and honest business that could be frequented and trusted by many people.