In the past, my Facebook wall showed me when a friend had made a new FB friend, and also told me who that friend was. Now, my wall does not show when any of my friends make a new friend. This only shows up on my ticker, which I never check.
You can add them to the list Close friends. Every action of them will be shown, including adding new friends or following someone. No one know your Close friends list, neither those in this list.
But you will be able to see such notifications only if your friends allows to share it with their friends.
If you have a list of friends you want to see this information about - add them into a list from here + click on Create List. One option is the to add them to a list called Close Friends, as Shinigamae suggested. I prefer a custom list, since Close Friends will notify you on any post they make and will probably make you feed centered around these people (it's a Facebook list).
After doing this friend-adding activity you can just navigate to your lists (with the same link from before), pick a list and see all their activity (not just which friend they have added).