在iOS 8和Swift 2.0中，请尝试这个，

override func tableView(tableView: UITableView, canEditRowAtIndexPath indexPath: NSIndexPath) -> Bool {
   // let the controller to know that able to edit tableView's row 
   return true
}

override func tableView(tableView: UITableView, commitEdittingStyle editingStyle UITableViewCellEditingStyle, forRowAtIndexPath indexPath: NSIndexPath)  {
   // if you want to apply with iOS 8 or earlier version you must add this function too. (just left in blank code)
}

override func tableView(tableView: UITableView, editActionsForRowAtIndexPath indexPath: NSIndexPath) -> [UITableViewRowAction]?  {
   // add the action button you want to show when swiping on tableView's cell , in this case add the delete button.
   let deleteAction = UITableViewRowAction(style: .Default, title: "Delete", handler: { (action , indexPath) -> Void in

   // Your delete code here.....
   .........
   .........
   })

   // You can set its properties like normal button
   deleteAction.backgroundColor = UIColor.redColor()

   return [deleteAction]
}

@Kurbz的回答很棒，但我想留下这张纸条，希望这个答案可以节省人们一些时间。

我的控制器中偶尔会出现这些线条，它们会导致滑动功能无法工作。

- (UITableViewCellEditingStyle)tableView:(UITableView *)tableView editingStyleForRowAtIndexPath:(NSIndexPath *)indexPath{
    return UITableViewCellEditingStyleNone; 
}

如果你使用UITableViewCellEditingStyleInsert或UITableViewCellEditingStyleNone作为编辑样式，那么滑动功能就不起作用了。你只能使用UITableViewCellEditingStyleDelete，这是默认的样式。

- (void)tableView:(UITableView *)tableView commitEditingStyle:(UITableViewCellEditingStyle)editingStyle forRowAtIndexPath:(NSIndexPath *)indexPath 
{
    if (editingStyle == UITableViewCellEditingStyleDelete)
    {
        //add code here for when you hit delete
        [dataSourceArray removeObjectAtIndex:indexPath.row];
        [tableView deleteRowsAtIndexPaths:@[indexPath] withRowAnimation:UITableViewRowAnimationAutomatic];
    }    
}    

SWIFT 5:适用于iOS 13+

func tableView(_ tableView: UITableView, canEditRowAt indexPath: IndexPath) -> Bool {
        return true
  }
    
    
 func tableView(_ tableView: UITableView, trailingSwipeActionsConfigurationForRowAt indexPath: IndexPath) -> UISwipeActionsConfiguration? {
        let deleteAction = UIContextualAction(style: .destructive, title: "Delete") {  (contextualAction, view, boolValue) in
            //Code I want to do here
        }
        
        let editAction = UIContextualAction(style: .destructive, title: "Edit") {  (contextualAction, view, boolValue) in
            //Code I want to do here
        }
        
        let swipeActions = UISwipeActionsConfiguration(actions: [deleteAction, editAction])
        
        return swipeActions
    }

Swift 2.2:

override func tableView(tableView: UITableView, canEditRowAtIndexPath indexPath: NSIndexPath) -> Bool {
    return true
}

override func tableView(tableView: UITableView,
    editActionsForRowAtIndexPath indexPath: NSIndexPath) -> [UITableViewRowAction]? {
    let delete = UITableViewRowAction(style: UITableViewRowActionStyle.Default, title: "DELETE"){(UITableViewRowAction,NSIndexPath) -> Void in

    print("Your action when user pressed delete")
}
let edit = UITableViewRowAction(style: UITableViewRowActionStyle.Normal, title: "EDIT"){(UITableViewRowAction,NSIndexPath) -> Void in

    print("Your action when user pressed edit")
}
    return [delete, block]
}

我知道这是一个老问题，但是@Kurbz的答案只需要Xcode 6.3.2和SDK 8.3

我需要添加[tableView beginUpdates]和[tableView endpdates](感谢@bay。phillips)

// Override to support editing the table view.
- (void)tableView:(UITableView *)tableView commitEditingStyle: (UITableViewCellEditingStyle)editingStyle forRowAtIndexPath:(NSIndexPath *)indexPath {
    // Open "Transaction"
    [tableView beginUpdates];

    if (editingStyle == UITableViewCellEditingStyleDelete) {
        // your code goes here
        //add code here for when you hit delete
        [tableView deleteRowsAtIndexPaths:@[indexPath] withRowAnimation:UITableViewRowAnimationFade];
     }

    // Close "Transaction"
    [tableView endUpdates];
}