Add the Alexa widget on your website and your rank will come down, the more traffic the lower your rank will be. Thanks Brian
Alexa rank is based on the daily Page Views of the site. You can increase Alexa rank by driving lots of traffic to your blog/site. Alexa rank update daily so you have to be focused on your blog traffic.
You can find more information if you search that in google But you can increase and hence it via bookmarking the links.
Alexa deals with site popularity so simply make sure site more popular! The goal is to get top 100k and once you have done that top 50k! That, my friend, is easier said than done though!
Alexa is number of visits or hits to your website. Increasing Alexa rank is by getting more traffic. Also there are some balckhat softwares which can improve your Alexa ranking and i don't suggest them as they are blackhat techniques.
Content quality will bring more traffic to your site but don`t depend on alexa, use google analytic instead