There are many ways to promote blog, one of them by promoting blog on facebook.
Facebook is the best choice to promote your blog, there many ways to promote your blog on facebook, some of them are:
1. Post your blog address or url on your facebook wall
2. Post your blog address or url on facebook information box.
3. post blog address or url on group wall
4. post your blog address or url when chatting
5. share your blog address or url to your friends
6. Send a blog address or url as a message to your friends
Note: I haven't known yet about google program policy about share link on facebook, so if you have google adsense of your blog, I suggest you not to do this trick.