Making a “continue reading” link for longer post

I really like this feature that I have seen on https://www.1976design.com and https://www.mezzoblue.com, but I haven’t really seen any WP sites that do this. You can see in these two examples that the post goes on for a few sentences and then a link asks the user to click to continue reading. This takes you to the permanent link of the post, where the entire post can be read. Obviously helps to cut down on the size of your first page and makes it more tidy for people just browsing through..
Anyhow, I am a PHP idiot. How can this be done using WP???