Well Alexa rank is a estimation of your website's daily traffic (Google is first at the moment). So the real question is how do you increase this traffic? Obviously one of the main factors is going to be the quality of the site and its contents. You could either buy more traffic (if your sole goal is to boost the ranking), try improving your SEO install the
Alexa toolbar. Good SEO is not easy to do and there are people offering these services. If you have money to invest then the combination of all three will yield results.