In Facebook, I often have posts titled "Your friend liked this" and the thing they liked is from a page that I don't follow or interact with.
How can I stop Facebook from adding these types of posts into my feed?
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Read this -> What does it mean to see first?
If this is your current setting and bothering you, changed it.
You cannot stop "Your friend liked this" notification directly from your News Feed. This is your friends activity, to stop this you have to unfollow your friends.
Note: If you unfollow someone, you will not be able to see any update from that person on your News Feed.
Facebook does not offer a built in method of doing this in their own interface. There is however a safe and free browser add-on called FB Purity that lets you filter out newsfeed posts depending on what type of post it is.
Once you have installed it, have a look at the User Guide page, to learn how to access the FBP options, and select the required Newsfeed filters you wish to use.
There are multiple options for filtering out "friend x liked post y" type posts, depending on the type of post, that is to say, whether it is a status a photo, a link etc.
You can get FB Purity here: http://fbpurity.com