The simplest thing to do is to keep adding quality content to your blog. After that I would start looking into blacking or social media promotion.
And you need a lot of contents too if you want to target Google (SEO). If you want something really fast, try paid advertising like Adwords or FB Ads. Facebook fan page & Twitter can be good as well but much slower than paid ones.
A simple technique that others overlook is commenting on other blogs. Make sure it's on popular blogs. Post your URL in it if it's a relevant page to yours, but don't spam! People will click on your URL and be taken to your blog. Simple but effective if done right.
I agree with adding content. Use good keywords within that content. And keep creating well placed backlinks to your blog.
I believe this is the best way to do what you're after. As long as you provide detailed comments, you won't be marked as spam. It's a great way to get loaded link juice for SEO if that's what you want to do. But other than that, make sure your blog is set up to spread socially with the buttons and whatnot, then pay for some google ads and hope it spreads.