Best way to accept multiple tcp clients?

So here is an answer that will get you started - which is more beginner level than my blog post.

.Net has an async pattern that revolves around a Begin* and End* call. For instance - BeginReceive and EndReceive. They nearly always have their non-async counterpart (in this case Receive); and achieve the exact same goal.

The most important thing to remember is that the socket ones do more than just make the call async - they expose something called IOCP (IO Completion Ports, Linux/Mono has these two but I forget the name) which is extremely important to use on a server; the crux of what IOCP does is that your application doesn't consume a thread while it waits for data.

How to Use The Begin/End Pattern

Every Begin* method will have exactly 2 more arguments in comparisson to it's non-async counterpart. The first is an AsyncCallback, the second is an object. What these two mean is, "here is a method to call when you are done" and "here is some data I need inside that method." The method that gets called always has the same signature, inside this method you call the End* counterpart to get what would have been the result if you had done it synchronously. So for example:

private void BeginReceiveBuffer()
{
   _socket.BeginReceive(buffer, 0, buffer.Length, BufferEndReceive, buffer);
}

private void EndReceiveBuffer(IAsyncResult state)
{
   var buffer = (byte[])state.AsyncState; // This is the last parameter.
   var length = _socket.EndReceive(state); // This is the return value of the method call.
   DataReceived(buffer, 0, length); // Do something with the data.
}

What happens here is .Net starts waiting for data from the socket, as soon as it gets data it calls EndReceiveBuffer and passes through the 'custom data' (in this case buffer) to it via state.AsyncResult. When you call EndReceive it will give you back the length of the data that was received (or throw an exception if something failed).

Better Pattern for Sockets

This form will give you central error handling - it can be used anywhere where the async pattern wraps a stream-like 'thing' (e.g. TCP arrives in the order it was sent, so it could be seen as a Stream object).

private Socket _socket;
private ArraySegment<byte> _buffer;
public void StartReceive()
{
    ReceiveAsyncLoop(null);
}

// Note that this method is not guaranteed (in fact
// unlikely) to remain on a single thread across
// async invocations.
private void ReceiveAsyncLoop(IAsyncResult result)
{
    try
    {
        // This only gets called once - via StartReceive()
        if (result != null)
        {
            int numberOfBytesRead = _socket.EndReceive(result);
            if(numberOfBytesRead == 0)
            {
                OnDisconnected(null); // 'null' being the exception. The client disconnected normally in this case.
                return;
            }

            var newSegment = new ArraySegment<byte>(_buffer.Array, _buffer.Offset, numberOfBytesRead);
            // This method needs its own error handling. Don't let it throw exceptions unless you
            // want to disconnect the client.
            OnDataReceived(newSegment);
        }

        // Because of this method call, it's as though we are creating a 'while' loop.
        // However this is called an async loop, but you can see it the same way.
        _socket.BeginReceive(_buffer.Array, _buffer.Offset, _buffer.Count, SocketFlags.None, ReceiveAsyncLoop, null);
    }
    catch (Exception ex)
    {
        // Socket error handling here.
    }
}

Accepting Multiple Connections

What you generally do is write a class that contains your socket etc. (as well as your async loop) and create one for each client. So for instance:

public class InboundConnection
{
    private Socket _socket;
    private ArraySegment<byte> _buffer;

    public InboundConnection(Socket clientSocket)
    {
        _socket = clientSocket;
        _buffer = new ArraySegment<byte>(new byte[4096], 0, 4096);
        StartReceive(); // Start the read async loop.
    }

    private void StartReceive() ...
    private void ReceiveAsyncLoop() ...
    private void OnDataReceived() ...
}

Each client connection should be tracked by your server class (so that you can disconnect them cleanly when the server shuts down, as well as search/look them up).