Alexa is traffic based. Increase your traffic and increase your ranking. It is that simple. If you see small sites with no value high in the rankings, it is because of recent news or events related to the site OR...electronic traffic. There are many tools out there that allow you to "create" visitors to your site. In the early days of Alexa, they actually were open about how to create "fake" traffic. Alexa no longer provides this information so...you are on your own there. Many still use this method to increase rankings which is just about the only way a great little site can compete with the big folks. Get all the ranking you want and have a bad site with no really valuable information and it will do no good.
Want better web results? First, create a great site and then check to see that your title, key words, and Meta's are good. (Use widexl.com to check your site) then, work 2-3 days a week at increasing and improving content. Link to your content on quality blogs and forums.....etc. etc. and you are on your way. It takes a huge commitment to operate a successful web sites (I find it important to have at least 3 unique sites) something that most pros are never able to do.