Alexa ranking completely depend on your web site traffic. I won't tell you crap tips to increase alexa rank like "install alexa toolbar", "Set your website as homepage on your home and office system" etc.

Content is king for good traffic. Write quality and unique content on your website and keep your web site updated.

In order to increase your Alexa rank, you should work only on driving as much traffic as possible to your web sie.

Always submit your web site pages to  social bookmarking sites like Digg, StumbleUpon, Delicious, Technorati etc.

Participate in relevant forums and use your website link as signature.

You should also submit your website to directories.