Delete a TableView + CoreData row

Then create a variable as follows:

lazy var fetchedResultsController: NSFetchedResultsController = {
    let fetchRequest = NSFetchRequest(entityName: "NomeDaSuaEntidade")
    fetchRequest.sortDescriptors = [NSSortDescriptor(key: "atributoParaOrdenar", ascending: true)]
    let fetchedResultsController = NSFetchedResultsController(fetchRequest: fetchRequest, managedObjectContext: self.sharedContext, sectionNameKeyPath: nil, cacheName: nil)
    return fetchedResultsController
}()

In viewDidLoad add the following code snippet:

...
do {
    try fetchedResultsController.performFetch()
} catch {}

fetchedResultsController.delegate = self
...

To populate the table in the cellForRowAtIndePath method retrieve the objects as follows:

...
let objeto = fetchedResultsController.objectAtIndexPath(indexPath) as! NomeDoSeuObjeto
...

In the numberOfRowsInSection method, retrieve the number of items as follows:

...
let sectionInfo = self.fetchedResultsController.sections![section]
return sectionInfo.numberOfObjects
...

Now the great charm of the NSFetchedResultController that makes it so worthwhile to use this delegate method that takes care of insertions, removals, updates and table row moves:

func controller(controller: NSFetchedResultsController, didChangeObject anObject: AnyObject, atIndexPath indexPath: NSIndexPath?, forChangeType type: NSFetchedResultsChangeType, newIndexPath: NSIndexPath?) {
    switch type {
    case .Insert:
        self.tableView.insertRowsAtIndexPaths([newIndexPath!], withRowAnimation: .Fade)
    case .Delete:
        self.tableView.deleteRowsAtIndexPaths([indexPath!], withRowAnimation: .Fade)
    case .Update:
        let cell = tableView.cellForRowAtIndexPath(indexPath!) as! ArtistCell
        let artist = controller.objectAtIndexPath(indexPath!) as! NomeDoSeuObjeto
        //preenche celula com dados do objeto
    case .Move:
        self.tableView.deleteRowsAtIndexPaths([indexPath!], withRowAnimation: .Fade)
        self.tableView.insertRowsAtIndexPaths([newIndexPath!], withRowAnimation: .Fade)
    }
}

Finally, add the following methods to make everything work perfectly:

func controllerWillChangeContent(controller: NSFetchedResultsController) {
    self.tableView.beginUpdates()
}

func controllerDidChangeContent(controller: NSFetchedResultsController) {
    self.tableView.endUpdates()
}