Keep building links back to your site. Social bookmarking, Guest Posting, High Profile backlinks, etc..
Why you want to increase your links in alexa? Alexa doesn't matter. Alexa will not give you traffic or revenue or any other thing. Its just a 3rd party site that determines the estimation traffic and backlinks of your site. Backlinks are the link backs to your site. When somebody links your site from his/her site, you get a backlink. Good Backlinks deliver traffic and helpful in SEO (Search Engine Optimization). I know you have just started, but you should google some of the basic terms and read stuff around to get some knowledge. Good Luck .
Simply get backlinks pointing to your website from other pages! Once alexa tracks them, and update your stats, they will show up
The only way to increase your link in Alexa is building your backlink network. But, any webmaster and seoer can see that, the number of link that listed in Alexa is not the true. Don't believe in that number, friends.
it should be "How can i increase my rank in Alexa" right???? LOL just start high PR link building and don't cut it down to only Do follow. think links are links. keep it in mind and start link building. thanks