Alexa themselves sell tools to help you optimise your online presence. These are mostly charged at a monthly rate and range from simple tools to check your listings to complicated programs to help you analyse your performance in detail. There are similar packages on offer from other companies.
To improve your ranking by yourself, there are some steps you can take. The main thing is to use Alexa as much as possible. So you can redirect traffic to Alexa, or use the Alexa toolbar when visiting your own website. This will have an effect on your ranking. Also, when you ask visitors to rate your website, give them a link to Alexa to do so.
If you put a free listing on DMOZ, you will also increase your visibility across the internet, though it may take a long time.
Check out the top rated websites on Alexa and review them yourself, redirecting users to your own website as you do so.
You can find more detailed advice, as well as a link to an ebook on this subject, here.