How to enable swipe to delete cell in a TableView?

As Dan has commented above, you need to implement the following table view delegate methods:

1. tableView:canEditRowAtIndexPath:
2. tableView:commitEditingStyle:forRowAtIndexPath:

Note: I have tried this in iOS 6 and iOS 7.

- (BOOL)tableView:(UITableView *)tableView canEditRowAtIndexPath:(NSIndexPath *)indexPath
{
    // Return YES - we will be able to delete all rows
    return YES;
}

- (void)tableView:(UITableView *)tableView commitEditingStyle:(UITableViewCellEditingStyle)editingStyle forRowAtIndexPath:(NSIndexPath *)indexPath
{
    // Perform the real delete action here. Note: you may need to check editing style
    //   if you do not perform delete only.
    NSLog(@"Deleted row.");
}