For many, selling links is a very popular technique for making money from a blog or website. There are also many companies that are engaged in managing or contacting a person you want to buy a link from the the seller (actually publisher).
Why do people buy links?
This question we seen in many forums and blog comments. The main reason is to achieve a better positioning of our site in the organic search results provided by Google.
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What company you recommend Monetize?
There are many companies those work as middleman (and takes money as fee too). Just search with the terms in Google and you will get a bunch of companies. Always search a review of that company from a good blog, before registration. We do not have any particular recommendation.
What do I need to sell links? Can you give me some recommendations to Monetize?
The first is sign up on their page and get approved.
Everything is based on the PR (PageRank) and Alexa rank, they do not understand that these have little value today, that is good for you, if you have an average site.

You need to have PR 4 or more and and a good Alexa rank (better if <1,00,000). Obviously, number of pageviews does matter. You need more than 2000 pageviews perday to see any real money. For this, you need to work on the SEO of your website first.
They understand quality of your website by seeking for keywords. They might search with chunk of text on random on Google to see if the content is unique.