MainWindow.xaml

<Window x:Class="SerialCommunication.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525">

    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition />
            <ColumnDefinition />
        </Grid.ColumnDefinitions>

        <TextBox Name="Message"
                 Grid.Column="0">
            Type here
        </TextBox>
        <Button Grid.Column="1"
                Click="Button_Click">
           Send to Arduino 
        </Button>
    </Grid>
</Window>

MainWindow.xaml.cs

using System;
using System.Collections.Generic;
using System.IO.Ports;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;

namespace SerialCommunication
{
    /// <summary>
    /// Interaction logic for MainWindow.xaml
    /// </summary>
    public partial class MainWindow : Window
    {
        private SerialPort _serialPort;

        public MainWindow()
        {
            InitializeComponent();

            _serialPort = new SerialPort("COM3", 9600);
            _serialPort.Open();


            this.Closed += new EventHandler(MainWindow_Closed);
        }

        void MainWindow_Closed(object sender, EventArgs e)
        {
	    // And close the serial port when we're finished
            _serialPort.Close();
        }

        private void Button_Click(object sender, RoutedEventArgs e)
        {
            // Send the text to the Arduino, byte by byte
            if (_serialPort.IsOpen)
            {
                _serialPort.Write(Message.Text);

		// Show anything out there!
                var foundMessage = _serialPort.ReadExisting();
                MessageBox.Show(foundMessage);
            }
        }
    }
}