You have a lot of different way to market your site. You can have it show up on search results (SEO), or on the ad space in search results (PPC). Can grow through social media, word of mouth, and I've had many times where a nice viral article on reddit can drive some great traffic to a site.
I would recommend finding someone that has experience in this type of service and pay them to do it unless you have the time to do it yourself. There are lots of stuff that goes into advertising and ranking a site. Some free things you can do is by directory submissions, link wheels, link exchanges and more. Just Google free or cheap advertising ideas.
Get into social media like facebook and Twitter. create accounts and target people around your niche. get into youtube and make videos about your site. There are so many options out there.
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There are plenty of ways to market your site online. Marketing through social media sites are gaining reputation to be a very good method in not marketing one's websites as well as getting direct traffic. If you are new to this and have no idea on the various marketing methods, then I suggest you go over the lessons we have on marketing techniques. The lessons cover marketing through social media sites as well as Web2.0 sites. I'm sure you'll get an idea or two. Hope that helps. Have a good day!