I don't want to explain what is Alexa. You came here because you know about Alexa and want to increase your Alexa Rank.
Easiest way to increase Alexa Rank is to install Alexa Site Widget in your blog. The widget will look like this:
Click on that widget and it will show the traffic chart and many other site related info. People have reported that within few days of installing the widget, their traffic has gone up significantly and this has improved their Alexa ranking!
Goto this link: http://www.alexa.com/siteowners/widgets to get the widget.
In that page, you will see a button "Build Widget" and adjacent to that is a text box. Enter your blog url in the text box and click on the button. It will give you a code and add that code in your blogger.