This article explains how to use Facebook's tool called "Recently Added" to see which users have been added by your friends in the last few weeks. While this feature is not available on the Facebook application, people using a phone or tablet can visit Facebook.com in a mobile browser and request the desktop version of the site to access this section.
Steps
Step 1. Visit https://www.facebook.com using a browser
If you are not already logged in, follow the onscreen instructions to log in.
You cannot see the "Recently added" section via application. If you are using a phone or tablet, press the browser menu icon and select Desktop site (or a similar option). This will open the same version of the site that you would see browsing on a computer.
Step 2. Open a friend's profile page
You can do this by clicking on their profile picture in the "News Section" or by doing a search.
Step 3. Click on Friends
This option is located on the left sidebar, under the "In brief" and "Photos" sections.
Step 4. Click on the Recently Added tab
It is located above the friends list, next to the "Mutual Friends" option. The friends recently added by that user will be displayed.