To re-add a deleted friend on Facebook, search for the person's name and send them another friend request. Finding someone on Facebook is typically accomplished by typing their name into the search bar at the top of the Facebook page. As long as the former friend has not been blocked, their name should appear near the top of the search results.
If a former friend has been blocked, they will need to be unblocked before a new friend request can be sent. If both parties have blocked each other, both users will have to adjust their settings before moving forward.
To block a friend, click the lock icon at the top of the Facebook page. Click the "How do I stop someone from bothering me?" tab, and then enter the name or email address of the person to be blocked and click the "Block" button. Friends will not be notified when they are blocked.
To unblock a friend, access the same tab and click the "View All Blocked Users" link. A window will appear with a list of blocked friends available to unblock. It can often take a few minutes to a few hours for the unblocked name to reappear in search results. If a person has been removed as a friend or blocked, they will be removed from items on a personal page, such as in relationship statuses.