I have a ViewModel which exposes the string property PageToolBarVisible which can be true or false:
You can put the BeginStoryboard inside your DataTrigger.EnterActions
<DataTrigger Binding="{Binding PageToolBarVisible}" Value="false">
<DataTrigger.EnterActions>
<BeginStoryboard>
<Storyboard>
<DoubleAnimation
Storyboard.TargetName="PageToolBar"
Storyboard.TargetProperty="(TextBlock.Opacity)"
From="0.0" To="1.0" Duration="0:0:3"/>
</Storyboard>
</BeginStoryboard>
</DataTrigger.EnterActions>
<DataTrigger.ExitActions>
<BeginStoryboard>
<Storyboard>
<DoubleAnimation
Storyboard.TargetName="PageToolBar"
Storyboard.TargetProperty="(TextBlock.Opacity)"
From="1.0" To="0.0" Duration="0:0:3"/>
</Storyboard>
</BeginStoryboard>
</DataTrigger.ExitActions>
</DataTrigger>