Both of these examples are with default value, you will find it in the constructor of model "Hello world!"

XAML datacontext

Add new WPF application project, add new model like:

namespace HelloWorldDataContext
{
    public class HelloWorldDataContextModel
    {
        public string HelloWorld { get; set; }

        public HelloWorldDataContextModel()
        {
            HelloWorld = "Hello world!";
        }
    }
}

Then XAML: 

<Window x:Class="HelloWorldDataContext.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:local="clr-namespace:HelloWorldDataContext"
        Title="MainWindow" Height="350" Width="525">
    <Window.Resources>
        <local:HelloWorldDataContextModel x:Key="HelloWorldDataContext" />
    </Window.Resources>
    <Grid DataContext="{StaticResource HelloWorldDataContext}">
        <TextBox HorizontalAlignment="Left" Height="23" Margin="222,127,0,0" TextWrapping="Wrap" Text="{Binding HelloWorld}" VerticalAlignment="Top" Width="120"/>
    </Grid>
</Window>

Important lines in XAML on which you should take care are:

xmlns:local="clr-namespace:HelloWorldDataContext"

Where name space is declared in model like:

namespace HelloWorldDataContext

<local:HelloWorldDataContextModel x:Key="HelloWorldDataContext" />

<Grid DataContext="{StaticResource HelloWorldDataContext}">

Example project you can download from here.

Programmatically setting datacontext

XAML: 

<Window x:Class="ProgramaticallyDataContext.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>
        <TextBox HorizontalAlignment="Left" Height="23" Margin="147,78,0,0" TextWrapping="Wrap" Text="{Binding HelloWorld}" VerticalAlignment="Top" Width="120"/>
    </Grid>
</Window>

Test Model is same like in above example, code behind (MainWindow.xaml.cs) is like: 

public MainWindow()
{
	InitializeComponent();

	HelloWorldDataContextModel objHW = new HelloWorldDataContextModel();
	objHW.HelloWorld = "Hello world";
	this.DataContext = objHW;
}

Example you can download from here.