Before I jump in too far, their first method of helping you earn money was Promoted Discovery. In promoted discovery, promoted links are placed in your discovery box at the bottom or even top of comment embeds based on the content on the page. Disqus uses a targeting algorithm that is improving every day, so eventually the service should become fairly solid.
Disqus made a page about the new program they are introducing, and you can see it here to get official documentation on how this works. If you keep on past the break, you can read more about this from Techman's World.
If your site links to Ecommerce sites frequently, then this new program from Disqus can help you and your site out a lot. Most of the time most outbound links are not affilated with you, and if a user purchases a product from your links you get no reward. Disqus works by using Viglink, a leader in affiliate link technology to make sure that your quality traffic to those sites are compensated. The exact technology and what is actually being done to your pages is yet to be found out, as I'm not enabling this on Techman's World and Disqus didn't specify that much. I did send Daniel Ha an email, so we'll see if we get a response. If a user makes a purchase on a product from your referral, you'll take a bit of the pie.
There is a minimum amount of money required before you get paid, however. You must earn a minimum of $100 before money is paid to you via your PayPal account. If you don't reach that limit, then....well I actually don't know what Disqus does with that money. I guess they either let it build up in your account or the keep it for themselves. I'll have to ask them about that as well.
There is no changes needed by you on your website. All you have to do is enable a simple setting in the discovery settings tab in the setting's area.
The update is live right now, so if you wish you can read more info by clicking the button below.