Facebook doesn't automatically show you all the content shared by your liked pages or even friends, and recently Facebook page owners have been experiencing extreme declines in audience reach. If there are pages or friends you always want to see updates for, here are the settings you should change.
Head to the Facebook page in question, then hover over the "Liked" button so you can click the "Get notifications" option. As Facebook explains on its help page, this setting notifes you (via red alert bubbles in the top right corner of any Facebook page) every time the person or page posts something shared with you.
To do this with your Facebook friends, click on the dropdown "Friends" button and click on "Get notifications".
Alternatively, you can add friends or pages to your "interests" lists. Click on the "Interests" link in the left menu from your home page, then "More" and you can add people or pages. This tells Facebook that you'd like to see this content, but it might not be 100 per cent foolproof, so for the most important ones, just use the notifications.
You could also create a RSS feed for Facebook pages, as MakeUseOf explains. That would deliver updates from Facebook pages to your RSS reader.