1.
install alexa toolbar and browse your blog every day. Ask your friends to do the same. Every time you browse your blog, Alexa Toolbar will communicate your visits to the Alexa Ranking Engine, which will update your ranking.

2.

set you blog as the home page for your browser.
and ask your friends, relatives to do the same.

3.

try to add webmasters category to your blog, because all webmasters already installed alexa toolbar, which will affect your rank when they visit your blog with alexa toolbar installed.

4.

Visit any website, blog or forum with related content( can be easily find by google ), leave your link there as comment or reply.

5.

Add alexa rank widget to your blog.

6.

Right article about alexa and encourage people to download the alexa toolbar.