How to animate Margin property in WPF

You can't animate Margin.Left (because Left is not a dependency property), but you can animate Margin. Use ObjectAnimationUsingKeyFrames:

<Storyboard x:Key="MoveMe">
    <ObjectAnimationUsingKeyFrames BeginTime="00:00:00" 
            Storyboard.TargetName="GroupTileSecond" 
            Storyboard.TargetProperty="Margin">
        <DiscreteObjectKeyFrame KeyTime="00:00:00">
            <DiscreteObjectKeyFrame.Value>
                <Thickness>134,70,0,0</Thickness>
            </DiscreteObjectKeyFrame.Value>
        </DiscreteObjectKeyFrame>
        <DiscreteObjectKeyFrame KeyTime="00:00:03">
            <DiscreteObjectKeyFrame.Value>
                <Thickness>50,70,0,0</Thickness>
            </DiscreteObjectKeyFrame.Value>
        </DiscreteObjectKeyFrame>
    </ObjectAnimationUsingKeyFrames>
</Storyboard>

There are some alternatives that allow you to use a DoubleAnimation, rather than key frames:

1. Place your target inside a Canvas, and animate its x position using Canvas.Left.
2. Apply a TranslateTransform to your target, and animate its x position using TranslateTransform.X.

Margin property can be animated using ThicknessAnimation

<Storyboard >
     <ThicknessAnimationUsingKeyFrames Storyboard.TargetProperty="Margin" BeginTime="00:00:00">
        <SplineThicknessKeyFrame KeyTime="00:00:00" Value="134, 70,0,0" />
        <SplineThicknessKeyFrame KeyTime="00:00:03" Value="50, 70,0,0" />
     </ThicknessAnimationUsingKeyFrames>
</Storyboard>

Actually, ya you can do what you want to do, exactly as you want to do using RenderTransform mixed with some DoubleAnimation and even add some extra flair to it, for example;

<Grid x:Name="TheObject" Opacity="0">
    <Grid.RenderTransform>
        <TranslateTransform x:Name="MoveMeBaby" X="50" />
    </Grid.RenderTransform>
    <Grid.Triggers>
        <EventTrigger RoutedEvent="Grid.Loaded">
            <BeginStoryboard>
                <Storyboard>
                    <DoubleAnimationUsingKeyFrames Storyboard.TargetName="MoveMeBaby" 
                                                   Storyboard.TargetProperty="X">
                        <SplineDoubleKeyFrame KeyTime="0:0:1.25" Value="0" />
                    </DoubleAnimationUsingKeyFrames>
                    <DoubleAnimationUsingKeyFrames Storyboard.TargetName="TheObject"
                                                   Storyboard.TargetProperty="Opacity">
                        <SplineDoubleKeyFrame KeyTime="0:0:1.55" Value="1" />
                    </DoubleAnimationUsingKeyFrames>
                </Storyboard>
            </BeginStoryboard>
        </EventTrigger>
    </Grid.Triggers>
</Grid>

Will move that object 50px on the X axis and even fade it in while it does so. Give it a shot and play with the values of the X property and the KeyTime to get what you want. Hope this helps, cheers.