You can unfriend someone on Facebook using either the Friends section of your own Timeline or the Friend button located on your friend’s Timeline. When you delete a friend, she is not sent a notification. However, she is removed from your friends list and you are removed from hers. If someone is harassing you on Facebook, use the Block feature to block that person from interacting with you entirely.
Unfriend Via Your Friend's Page
Step 1: Click your name on the main menu along the top of the Facebook website to load your Timeline.
Step 2: Click Friends to load your Friends panel, which contains a list of all of your friends.
Step 3: Enter in the Search field the name of the person you want to unfriend.
Step 4: Click the Friends button next to the person you want to unfriend and select Unfriend on the drop-down menu.
Unfriend Via the Person's Timeline
Step 1: Use the Find Friends field along the top of the page to search for the person you want to unfriend. Click the person’s name on the search results to load his Timeline.
Step 2: Click the Friends button on the right side of the person’s Timeline header image and select Unfriend to remove the person as your Facebook friend.
Deleting Facebook Friends on Your Mobile Device
To unfriend someone using the Web browser on your smartphone or tablet, you need visit the person’s profile page. Once you’re on the person’s profile, tap the Friends button and select Unfriend. The same process applies when un-friending people using the official Facebook app for iOS, Android and Windows Phone devices.
Blocking People on Facebook
If you no longer want someone to interact with you at all on Facebook, block him. Blocking a person on Facebook prevents him from adding you as a friend, sending you messages, seeing your Facebook profile, tagging you, and inviting you to events and groups.
To block someone, click the Privacy button on the main menu along the top of the Facebook website and select How Do I Stop Someone From Bothering Me. Enter the email address or name of the person you want to block and then click Block.
Bulk Friend Deletion
Facebook used to have a tool that enabled you to delete multiple friends at once. This bulk deletion tool is no longer available, as of publication. The quickest way to delete multiple friends is to use the Friends section of your Timeline as outlined above.
If you use the Google Chrome Web browser, there is an add-on called Facebook Mass Delete Friends that's designed to help you delete multiple friends relatively quickly. However, in practice, it offers essentially the same functionality available through the Friends section of your Timeline.