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.P
There are a few methods you could try (or combine). The first is to add friends or pages to your "interests" lists. Click on the "Interests" link in the left menu from your home page, then "More" and add the people or pages you most want to see updates from. This tells Facebook that you'd like to see this content, but it's not 100% foolproof.P
For the most important updates (e.g., your significant other), set up notifications for them. On your Facebook friends' profile, click on the dropdown "Friends" button and click on "Get notifications." You could also do this with Facebook pages—although depending on how much the page updates, you might end up getting more alerts than you care to dig through. On the Facebook page in question, 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.P
As commenter joesub notes below, you can instead add the pages and friends you like to their own lists and then favorite the lists. This might be the best method since it shows everything.P
Finally, you could also create a RSS feed for Facebook pages, as MakeUseOf explains. That would deliver updates from Facebook pages to your RSS reader.P