On Facebook I was trying to hide notifications from an application but I accidentally hit the person's name. How can I undo the hiding of a friend?
If you remove something from your Wall, it is gone forever and you cannot get it back.
If you have hidden a friend, page, or application from your News Feed and want to unhide it, then as MrGumbe noted you can scroll to the bottom of the News Feed and click Edit Options on the right side of the shaded bar. However the dialog that pops up is different depending on whether you were showing "Top News" or "Most Recent".
The "Top News" dialog has different tabs for hidden Friends, Pages, and Applications (if any are hidden). To unhide any of these, click the appropriate tab at the top if necessary and then click its "Add To News Feed" button.
The "Most Recent" dialog shows hidden friends and pages in the Hide column; click the "X" to unhide. It allows you to hide additional friends but does not have any way to control hidden applications.