Here is the storyboard that describes your sequence:
<Storyboard x:Key="animate">
<DoubleAnimationUsingKeyFrames BeginTime="00:00:00" Storyboard.TargetName="button1" Storyboard.TargetProperty="(UIElement.Opacity)">
<LinearDoubleKeyFrame KeyTime="00:00:00" Value="0"/>
<LinearDoubleKeyFrame KeyTime="00:00:03" Value="0.75"/>
</DoubleAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames BeginTime="00:00:00" Storyboard.TargetName="button1" Storyboard.TargetProperty="(UIElement.Visibility)">
<DiscreteObjectKeyFrame KeyTime="00:00:00" Value="Visibility.Visible"/>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames BeginTime="00:00:00" Storyboard.TargetName="control" Storyboard.TargetProperty="(UIElement.Visibility)">
<DiscreteObjectKeyFrame KeyTime="00:00:00" Value="Visibility.Visible"/>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
You can trigger it in xaml through EventTrigger or in code through TryFindResource().
Here is the link on Animation Overview MSDN Article and you can find there answers on your questions on many WPF animations topics.