Summarize the following:
Your contact's timeline and profile page will display onscreen. Going forward, that contact will no longer display in your Facebook timeline, and your own Facebook profile will also be removed from that particular contact's timeline.

Summary:
Sign in to your Facebook account at https://www.facebook.com/. Navigate to the "Friends" list in the left pane of your Facebook profile. Click on the profile of the contact or friend you want deleted from Facebook. Point to the button labeled "Friends" at the top of the contact's Facebook timeline. Select "Unfriend" from the list of options provided.