I'll add to this, since the question is about how to change a UIViewController into a UITableViewController, and given that this question is over a year old and the original answer, while valid and may or may not have been the only solution at the time, doesn't actually answer the question and is not the only solution.
It IS possible to do this, you just have to set up the table view delegate and datasource outlets in IB, and manually edit the storyboard XML, which sounds scary but is actually very easy.
First, change your class's parent to be a UITableViewController. UITableViewController already adopts the UITableViewDatasource and UITableViewDelegate protocols, so if your class does too you can remove them:
@implementation MyTableViewController : UITableViewController
...
@end
Next, create new referencing outlets on your UITableView for its dataSource and delegate. The easiest way to do this is to control-drag from the UITableView to itself. The popup will give you the dataSource and delegate options.
Lastly, you need to change the storyboard XML. The storyboard file can get pretty big pretty fast. The easiest way to find the scene you are looking for is by setting Storyboard Identifier in the Identity Inspector. To view the XML directly, right click on the storyboard file in the project navigator and select "Open As -> Source Code". Now just search for whatever you set the reuse identifier to earlier. You'll see something similar to this:
<!-- My Table View Controller -->
<scene sceneID="EuE-XX-cCb">
<objects>
<viewController storyboardIdentifier="MY_TABLE_VIEW_IDENTIFIER" ... >
// Lots of other stuff
</viewController>
</objects>
</scene>
All you need to do is change the opening and closing view controller tags
<viewController>
</viewController>
to be tableViewController instead
<tableViewController>
</tableViewController>
That's it! No need to create a new UITableViewController scene or embed a UITableViewController in a container view.
EDIT:
I should also add that the UITableView MUST be the root view. It cannot be embedded inside another UIView.