To increase traffic to your blog using facebook, you're going to need a lot of content. Your content needs to be high quality, no exception. Post fresh content on your fan page, profile and group 2 or more times a day.
Posting once a week or once per month works if you're already popular but if you're just starting out you need to post 2 or more times per day. This will also help you reach more people in different time zones.
Don't be afraid of posting the same post in different times, whoever complains tell them:
"you're spending too much time on social media, get a life"
haha... I'm just kidding
But what I'm saying is that you can post a piece of content 9am monday then re-post it wednesday 7pm.
In the past few days, I realized that some posts get a lot of shares, comments and likes in groups, while other get more engagement on a fan page and other on my profile. So it's a good idea to have all 3 (group, fan page and profile).
Mix your content with some funny images (memes) this will increase engagement and as people share that funny image it will bring more traffic to your facebook page, group and profile. Which will result in more traffic for your blog.
Finally, keep inviting new people. New people are the ones who always ask questions and that increases engagement. Some times old members answer questions I haven't saw or send the new member to a blog post or video I created in the past. So keep adding new people on a daily bases.
Yes, this is really time consuming but once you've built a good and engaging audience it will be much easier to promote your stuff in the future. Using paid ads will require you to use money each time you want to promote something, this is why I prefer free strategies.
Hope that helps.