Given the fact that Facebook has exceeded one billion of active users, let’s focus on this particular social network. For starters, just follow these few basic rules.
Facebook Page
Create so called Facebook Page (Facebook Page) for your digital magazine. Avoid conventional personal profile, which can only be used for a real person, not a “magazine”.
Tasting of contents
Publish advertisements for interesting content within the intervals between issue releases, motivate fans who have not already downloaded the current number to do so. Do not forget to provide add banners with page review or image. It works much better than simple text messages. See how Dotyk does it.
Backstage attractions
From time to time publish interesting photo or information from your backstage scenes. A lot of readers are interested in what is behind the final product, make a use of it.
New issue has been just published
When a new issue comes out, publish only professionally prepared graphical illustration. Remember that the cover page sells – pay attention to the design. An example of such illustration can be seen below. Additionally make a use of it also outside of Facebook.
Attention, important: do not forget to complement the image with text commentary, adding direct links for digital magazine download from Apple Appstore and Google Play. See example of tablet magazine Architual. 
Share your contents
Do you have a personal profile on Facebook? Take advantage of your friends, and share interesting news from Facebook pages to your digital magazine.
Hashtags
You may place so called hashtags to the text of your Facebook contribution – keywords with preceding character “#”. For example, for an architecture magazine, you could use the #digitaljournal #architecture #digitalmagazine. Such labeled keywords become clickable on Facebook and allow you or anyone else to freely move between various contributions from different people and pages with particular topic. Your contribution will thus reach completely new potential readers. See below here. However be careful, not to overdo it with tags so you are not spaming.
Take the points mentioned here as an information minimum to get started with the promotion. Educate yourself on the Internet (there are piles of articles about Facebook marketing), you can also pay for training, or may be inspired by competition.