An Objective-C delegate is an object that has been assigned to the delegate property another object. To create one, you define a class that implements the delegate methods you're interested in, and mark that class as implementing the delegate protocol.

For example, suppose you have a UIWebView. If you'd like to implement its delegate's webViewDidStartLoad: method, you could create a class like this:

@interface MyClass<UIWebViewDelegate>
// ...
@end

@implementation MyClass
- (void)webViewDidStartLoad:(UIWebView *)webView { 
    // ... 
}
@end

Then you could create an instance of MyClass and assign it as the web view's delegate:

MyClass *instanceOfMyClass = [[MyClass alloc] init];
myWebView.delegate = instanceOfMyClass;

On the UIWebView side, it probably has code similar to this to see if the delegate responds to the webViewDidStartLoad: message using respondsToSelector: and send it if appropriate.

if([self.delegate respondsToSelector:@selector(webViewDidStartLoad:)]) {
    [self.delegate webViewDidStartLoad:self];
}

The delegate property itself is typically declared weak (in ARC) or assign (pre-ARC) to avoid retain loops, since the delegate of an object often holds a strong reference to that object. (For example, a view controller is often the delegate of a view it contains.)

Making Delegates for Your Classes

To define your own delegates, you'll have to declare their methods somewhere, as discussed in the Apple Docs on protocols. You usually declare a formal protocol. The declaration, paraphrased from UIWebView.h, would look like this:

@protocol UIWebViewDelegate <NSObject>
@optional
- (void)webViewDidStartLoad:(UIWebView *)webView;
// ... other methods here
@end

This is analogous to an interface or abstract base class, as it creates a special type for your delegate, UIWebViewDelegate in this case. Delegate implementors would have to adopt this protocol:

@interface MyClass <UIWebViewDelegate>
// ...
@end

And then implement the methods in the protocol. For methods declared in the protocol as @optional (like most delegate methods), you need to check with -respondsToSelector: before calling a particular method on it.

Naming

Delegate methods are typically named starting with the delegating class name, and take the delegating object as the first parameter. They also often use a will-, should-, or did- form. So, webViewDidStartLoad: (first parameter is the web view) rather than loadStarted (taking no parameters) for example.

Speed Optimizations

Instead of checking whether a delegate responds to a selector every time we want to message it, you can cache that information when delegates are set. One very clean way to do this is to use a bitfield, as follows:

@protocol SomethingDelegate <NSObject>
@optional
- (void)something:(id)something didFinishLoadingItem:(id)item;
- (void)something:(id)something didFailWithError:(NSError *)error;
@end

@interface Something : NSObject
@property (nonatomic, weak) id <SomethingDelegate> delegate;
@end

@implementation Something {
  struct {
    unsigned int didFinishLoadingItem:1;
    unsigned int didFailWithError:1;
  } delegateRespondsTo;
}
@synthesize delegate;

- (void)setDelegate:(id <SomethingDelegate>)aDelegate {
  if (delegate != aDelegate) {
    delegate = aDelegate;

    delegateRespondsTo.didFinishLoadingItem = [delegate respondsToSelector:@selector(something:didFinishLoadingItem:)];
    delegateRespondsTo.didFailWithError = [delegate respondsToSelector:@selector(something:didFailWithError:)];
  }
}
@end

Then, in the body, we can check that our delegate handles messages by accessing our delegateRespondsTo struct, rather than by sending -respondsToSelector: over and over again.

Informal Delegates

Before protocols existed, it was common to use a category on NSObject to declare the methods a delegate could implement. For example, CALayer still does this:

@interface NSObject(CALayerDelegate)
- (void)displayLayer:(CALayer *)layer;
// ... other methods here
@end

This tells the compiler that any object might implement displayLayer:.

You would then use the same -respondsToSelector: approach as described above to call this method. Delegates implement this method and assign the delegate property, and that's it (there's no declaring you conform to a protocol). This method is common in Apple's libraries, but new code should use the more modern protocol approach above, since this approach pollutes NSObject (which makes autocomplete less useful) and makes it hard for the compiler to warn you about typos and similar errors.

Important: This check should always be performed asynchronously. The majority of answers below are synchronous so be careful otherwise you'll freeze up your app.

Swift

1. Install via CocoaPods or Carthage: https://github.com/ashleymills/Reachability.swift

2. Test reachability via closures

   let reachability = Reachability()!
   
   reachability.whenReachable = { reachability in
       if reachability.connection == .wifi {
           print("Reachable via WiFi")
       } else {
           print("Reachable via Cellular")
       }
   }
   
   reachability.whenUnreachable = { _ in
       print("Not reachable")
   }
   
   do {
       try reachability.startNotifier()
   } catch {
       print("Unable to start notifier")
   }
   

Objective-C

1. Add SystemConfiguration framework to the project but don't worry about including it anywhere

2. Add Tony Million's version of Reachability.h and Reachability.m to the project (found here: https://github.com/tonymillion/Reachability)

3. Update the interface section

   #import "Reachability.h"
   
   // Add this to the interface in the .m file of your view controller
   @interface MyViewController ()
   {
       Reachability *internetReachableFoo;
   }
   @end
   

4. Then implement this method in the .m file of your view controller which you can call

   // Checks if we have an internet connection or not
   - (void)testInternetConnection
   {
       internetReachableFoo = [Reachability reachabilityWithHostname:@"www.google.com"];
   
       // Internet is reachable
       internetReachableFoo.reachableBlock = ^(Reachability*reach)
       {
           // Update the UI on the main thread
           dispatch_async(dispatch_get_main_queue(), ^{
               NSLog(@"Yayyy, we have the interwebs!");
           });
       };
   
       // Internet is not reachable
       internetReachableFoo.unreachableBlock = ^(Reachability*reach)
       {
           // Update the UI on the main thread
           dispatch_async(dispatch_get_main_queue(), ^{
               NSLog(@"Someone broke the internet :(");
           });
       };
   
       [internetReachableFoo startNotifier];
   }
   

Important Note: The Reachability class is one of the most used classes in projects so you might run into naming conflicts with other projects. If this happens, you'll have to rename one of the pairs of Reachability.h and Reachability.m files to something else to resolve the issue.

Note: The domain you use doesn't matter. It's just testing for a gateway to any domain.