Driving traffic through Social Media to your blog, can be done in various ways:
1- Add Social Media share buttons to your blog allowing others to share your blog with their tribe through Social Media. This is very easy and effective way as you are getting people to endorse you and hence adds credibility to your blog and as a result more traffic
2- As soon as you write your blog post share it with your tribe on the various Social Media platforms. Use URL shorting tools so you can track which platform is most effective for you. Additionally, share it in many different ways so you grab the attention of different target markets.
3- RSS feed your blog to your Facebook page and also Twitter
4- Interact with other blog owners that have relevant interesting topics that compliment or add to your blog
There are other ways I guess but this is what I can think of for now.