You can improve your site/blog's alexa rank by :
1- Putting an alexa rank widget in your website/blog ( an example is the one at the bottom of the page ) Enter Here
2- Installing the alexa toolbar on your browser . Why ? since the more people that enter your blog/website having on their browser the alxa toolbar ( including you ) the more your blog/site's alexa rank will improve . Enter Here For installing the toolbar
3- Increasing your backlinks ofcourse . This might help you
4- Adding a stumble upon widget and or digg widget to your posts in your blog/site ( stumble upon , digg )
5- Increasing traffic in general through youtube , social networks , SEO ...