Programmatically Add CenterX/CenterY Constraints

Update for Swift 3/Swift 4:

As of iOS 8, you can and should activate your constraints by setting their isActive property to true. This enables the constraints to add themselves to the proper views. You can activate multiple constraints at once by passing an array containing the constraints to NSLayoutConstraint.activate()

let label = UILabel(frame: CGRect.zero)
label.text = "Nothing to show"
label.textAlignment = .center
label.backgroundColor = .red  // Set background color to see if label is centered
label.translatesAutoresizingMaskIntoConstraints = false
self.tableView.addSubview(label)

let widthConstraint = NSLayoutConstraint(item: label, attribute: .width, relatedBy: .equal,
                                         toItem: nil, attribute: .notAnAttribute, multiplier: 1.0, constant: 250)

let heightConstraint = NSLayoutConstraint(item: label, attribute: .height, relatedBy: .equal,
                                          toItem: nil, attribute: .notAnAttribute, multiplier: 1.0, constant: 100)

let xConstraint = NSLayoutConstraint(item: label, attribute: .centerX, relatedBy: .equal, toItem: self.tableView, attribute: .centerX, multiplier: 1, constant: 0)

let yConstraint = NSLayoutConstraint(item: label, attribute: .centerY, relatedBy: .equal, toItem: self.tableView, attribute: .centerY, multiplier: 1, constant: 0)

NSLayoutConstraint.activate([widthConstraint, heightConstraint, xConstraint, yConstraint])

Better Solution:

Since this question was originally answered, layout anchors were introduced making it much easier to create the constraints. In this example I create the constraints and immediately activate them:

label.widthAnchor.constraint(equalToConstant: 250).isActive = true
label.heightAnchor.constraint(equalToConstant: 100).isActive = true
label.centerXAnchor.constraint(equalTo: self.tableView.centerXAnchor).isActive = true
label.centerYAnchor.constraint(equalTo: self.tableView.centerYAnchor).isActive = true

or the same using NSLayoutConstraint.activate():

NSLayoutConstraint.activate([
    label.widthAnchor.constraint(equalToConstant: 250),
    label.heightAnchor.constraint(equalToConstant: 100),
    label.centerXAnchor.constraint(equalTo: self.tableView.centerXAnchor),
    label.centerYAnchor.constraint(equalTo: self.tableView.centerYAnchor)
])

Note: Always add your subviews to the view hierarchy before creating and activating the constraints.

Original Answer:

The constraints make reference to self.tableView. Since you are adding the label as a subview of self.tableView, the constraints need to be added to the "common ancestor":

   self.tableView.addConstraint(xConstraint)
   self.tableView.addConstraint(yConstraint)

As @mustafa and @kcstricks pointed out in the comments, you need to set label.translatesAutoresizingMaskIntoConstraints to false. When you do this, you also need to specify the width and height of the label with constraints because the frame no longer is used. Finally, you also should set the textAlignment to .Center so that your text is centered in your label.

    var  label = UILabel(frame: CGRectZero)
    label.text = "Nothing to show"
    label.textAlignment = .Center
    label.backgroundColor = UIColor.redColor()  // Set background color to see if label is centered
    label.translatesAutoresizingMaskIntoConstraints = false
    self.tableView.addSubview(label)

    let widthConstraint = NSLayoutConstraint(item: label, attribute: .Width, relatedBy: .Equal,
        toItem: nil, attribute: .NotAnAttribute, multiplier: 1.0, constant: 250)
    label.addConstraint(widthConstraint)

    let heightConstraint = NSLayoutConstraint(item: label, attribute: .Height, relatedBy: .Equal,
        toItem: nil, attribute: .NotAnAttribute, multiplier: 1.0, constant: 100)
    label.addConstraint(heightConstraint)

    let xConstraint = NSLayoutConstraint(item: label, attribute: .CenterX, relatedBy: .Equal, toItem: self.tableView, attribute: .CenterX, multiplier: 1, constant: 0)

    let yConstraint = NSLayoutConstraint(item: label, attribute: .CenterY, relatedBy: .Equal, toItem: self.tableView, attribute: .CenterY, multiplier: 1, constant: 0)

    self.tableView.addConstraint(xConstraint)
    self.tableView.addConstraint(yConstraint)

Center in container

The code below does the same thing as centering in the Interface Builder.

override func viewDidLoad() {
    super.viewDidLoad()

    // set up the view
    let myView = UIView()
    myView.backgroundColor = UIColor.blue
    myView.translatesAutoresizingMaskIntoConstraints = false
    view.addSubview(myView)

    // Add code for one of the constraint methods below
    // ...
}

Method 1: Anchor Style

myView.centerXAnchor.constraint(equalTo: view.centerXAnchor).isActive = true
myView.centerYAnchor.constraint(equalTo: view.centerYAnchor).isActive = true

Method 2: NSLayoutConstraint Style

NSLayoutConstraint(item: myView, attribute: NSLayoutConstraint.Attribute.centerX, relatedBy: NSLayoutConstraint.Relation.equal, toItem: view, attribute: NSLayoutConstraint.Attribute.centerX, multiplier: 1, constant: 0).isActive = true
NSLayoutConstraint(item: myView, attribute: NSLayoutConstraint.Attribute.centerY, relatedBy: NSLayoutConstraint.Relation.equal, toItem: view, attribute: NSLayoutConstraint.Attribute.centerY, multiplier: 1, constant: 0).isActive = true

Notes

• Anchor style is the preferred method over NSLayoutConstraint Style, however it is only available from iOS 9, so if you are supporting iOS 8 then you should still use NSLayoutConstraint Style.
• You will also need to add length and width constraints.
• My full answer is here.

The ObjectiveC equivalent is:

    myView.translatesAutoresizingMaskIntoConstraints = NO;

    [[myView.centerXAnchor constraintEqualToAnchor:self.view.centerXAnchor] setActive:YES];

    [[myView.centerYAnchor constraintEqualToAnchor:self.view.centerYAnchor] setActive:YES];

In Swift 5 it looks like this:

label.translatesAutoresizingMaskIntoConstraints = false
label.centerXAnchor.constraint(equalTo: vc.view.centerXAnchor).isActive = true
label.centerYAnchor.constraint(equalTo: vc.view.centerYAnchor).isActive = true

Programmatically you can do it by adding the following constraints.

NSLayoutConstraint *constraintHorizontal = [NSLayoutConstraint constraintWithItem:self  
                                                                      attribute:NSLayoutAttributeCenterX 
                                                                      relatedBy:NSLayoutRelationEqual 
                                                                         toItem:self.superview 
                                                                      attribute:attribute 
                                                                     multiplier:1.0f 
                                                                       constant:0.0f];

NSLayoutConstraint *constraintVertical = [NSLayoutConstraint constraintWithItem:self
                                                                        attribute:NSLayoutAttributeCenterY 
                                                                        relatedBy:NSLayoutRelationEqual
                                                                           toItem:self.superview 
                                                                        attribute:attribute 
                                                                       multiplier:1.0f
                                                                         constant:0.0f];