This one is my favorite.

If you want to sell premium membership to your free users, don’t expect they will come to you without seeing any value addition.  You need to constantly remind them of what they are missing every week/ month. You can periodically show them some glimpse of what you are offering to premium users.  

Let them know that your services are worth enough to shell some bucks.

Showing notifications like below are just an example of newsletter hacks you can do to convert them.  But it’s applicable to pretty much any business.   

How you should do it?

Do this with some personalization. This will create 2 types of impact: 

   1. Imperative Impact of losing out (FOMO). It's evident that now you know that the thing is there and you want it.  What is in between some X bucks? Just get it.
 
   2. A long-lasting bond of activity, shows you are active and regularly delivering the quality stuff, The more articles or stuffs your deliver (the more the content) the stronger will be the bond. That's where personalization matters.