There are three different ways of consuming messages received by the library.

1. Polling

If you already have an application loop for your game this would be the most suitable to use; just call ReadMessage() until it returns null.

NetIncomingMessage msg;
while ((msg = peer.ReadMessage()) != null)
{
   // process message here
}

2. Callback

If your application is completely event/UI-driven and does not have an application loop per se, you can register a callback to fire when a message arrives. The registration must happen from the correct SynchronizationContext (ie. call RegisterReceivedCallback from the same thread you want to receive the message notification on)

peer.RegisterReceivedCallback(new SendOrPostCallback(GotMessage)); 

public static void GotMessage(object peer)
{
	var msg = peer.ReadMessage();
	// process message here
}	

3. EventWaitHandle

If your incoming message processing is run on a separate thread you can use the MessageReceivedEvent property to have your thread block until an incoming message arrives.

// in your separate thread
peer.MessageReceivedEvent.WaitOne(); // this will block until a message arrives

var msg = peer.ReadMessage();
// process message here