Use DependencyProperties and bind them to your View.
Short cut is : propdp + tab
For Example:
public partial class MainWindow : Window
    {
        public string MyName
        {
            get { return (string)GetValue(MyNameProperty); }
            set { SetValue(MyNameProperty, value); }
        }
        // Using a DependencyProperty as the backing store for MyName.  This enables animation, styling, binding, etc...
        public static readonly DependencyProperty MyNameProperty =
            DependencyProperty.Register("MyName", typeof(string), typeof(MainWindow), new PropertyMetadata(string.Empty));
        public MainWindow()
        {
            InitializeComponent();
            MyName = "The main window.";
        }
    }
View:
<Window x:Class="WpfTest.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:WpfTest"
        mc:Ignorable="d"
        Title="MainWindow" Height="350" Width="525"
        x:Name="Root">
    <TextBlock Text="{Binding MyName, ElementName=Root, Mode=OneWay}" />
</Window>
Anyway please check out MVVM and for extended information What is a DepdencyProperty ?