Example of how to search a UITableView in iOS 5 and iOS 6
I've been pulling my hair out how to do this and finally worked it out. You can read a step by step guide here:
http://wpguru.co.uk/2013/02/how-to-create-a-searchable-uitableview/
I've also added ways to initially hide the search bar, and hide it again when the user is finished searching as explained here:
http://wpguru.co.uk/2013/03/how-to-hide-and-show-the-uisearchbar-in-a-uitableview/
Enjoy!