To check your link popularity score, simply go to a website that offers the service, type in your URL, and hit the submit button.
To check the websites linking back to you on a search engine, just type “link:yourdomain.com” and it will show up in the search results. Most search engines support this.
How To Increase Your Link Popularity
Getting links to your website isn't going to happen overnight unless you run a huge website of some sort.
The first thing that you should do is put up quality content. If you have quality content, quality websites will link to your website. Some search engines like Google look at the website that's linking to your website in addition to looking at yours. All of this will factor in the search results.
You can also email webmasters whom run websites similar to yours and ask if they would like to exchange links. This method is a more “hands-on” method in comparison with the first one. Of course, you would still need the quality content though.
Another thing that you can do is submit your website URL to a variety of directories. You can submit to a couple directories or a couple hundred or even thousand directories. There are services that you can pay for and they will submit your website for you to a list of directories