Organic search traffic can take up to 6 months. But to really get going with organic search traffic can take up to a year or more.
Expect it to take at least 18 months at the minimum to start seeing good search traffic from google and other search engines.
You need lots of great content too. So while waiting keep posting more content to your website and overtime you should see your website traffic grow.
Make sure it's quality content though and not just content just thrown up on your blog.
It has to be useful. Google favors quality content.