You may have seen some sites that has a Alexa button displaying the site Alexa ranking plus other statistics. For example, I have installed such a button in this blog: Generating Revenue from your website. The button is at the bottom of the left sidebar.
This is best done with a browser with tabbed browsing like Firefox as you can use one tab for your Blogger Dashboard and another tab for the Alexa site where you can generate the necessary script. You can install Firefox with Google toolbar by clicking on the "Browse the web better. Get Firefox with Google toolbar" link at the top of the right sidebar. If you are using Firefox to view this post, you can right-click on a link and select "Open in new tab".
If you are still using the old classic Blogger template, you will have to paste the script direct into the template. Use this post (will complete this post later when I get access to my own computer where I have all the post URLs saved in an Excel file).