How can I add a hint text to WPF textbox?

You can accomplish this much more easily with a VisualBrush and some triggers in a Style:

<TextBox>
    <TextBox.Style>
        <Style TargetType="TextBox" xmlns:sys="clr-namespace:System;assembly=mscorlib">
            <Style.Resources>
                <VisualBrush x:Key="CueBannerBrush" AlignmentX="Left" AlignmentY="Center" Stretch="None">
                    <VisualBrush.Visual>
                        <Label Content="Search" Foreground="LightGray" />
                    </VisualBrush.Visual>
                </VisualBrush>
            </Style.Resources>
            <Style.Triggers>
                <Trigger Property="Text" Value="{x:Static sys:String.Empty}">
                    <Setter Property="Background" Value="{StaticResource CueBannerBrush}" />
                </Trigger>
                <Trigger Property="Text" Value="{x:Null}">
                    <Setter Property="Background" Value="{StaticResource CueBannerBrush}" />
                </Trigger>
                <Trigger Property="IsKeyboardFocused" Value="True">
                    <Setter Property="Background" Value="White" />
                </Trigger>
            </Style.Triggers>
        </Style>
    </TextBox.Style>
</TextBox>

To increase the re-usability of this Style, you can also create a set of attached properties to control the actual cue banner text, color, orientation etc.

This is my simple solution, adapted from Microsoft (https://code.msdn.microsoft.com/windowsapps/How-to-add-a-hint-text-to-ed66a3c6)

    <Grid Background="White" HorizontalAlignment="Right" VerticalAlignment="Top"  >
        <!-- overlay with hint text -->
        <TextBlock Margin="5,2" MinWidth="50" Text="Suche..." 
                   Foreground="LightSteelBlue" Visibility="{Binding ElementName=txtSearchBox, Path=Text.IsEmpty, Converter={StaticResource MyBoolToVisibilityConverter}}" IsHitTestVisible="False"/>
        <!-- enter term here -->
        <TextBox MinWidth="50" Name="txtSearchBox" Background="Transparent" />
    </Grid>