How do I know the exact day I added a friend on Facebook?

There are two ways to check the exact day when you added a friend on facebook,

If you go your friend’s Timeline, click the ellipsis (3 dots) at the lower right of the Cover Photo and select See Friendship you can get the Month/Year of the friend request acceptance.

Then go to your Timeline and use your Activity Log,  (filtering it with Frends) you can use the year in the right column to auto scroll back to the general time and search the month to find the date you became friends.