The best way is to define a new button template. Adding this to your UserControl.Resources tag should work:
<ControlTemplate x:Key="ButtonControlTemplate1" TargetType="Button">
<Grid>
<vsm:VisualStateManager.VisualStateGroups>
<vsm:VisualStateGroup x:Name="CommonStates">
<vsm:VisualState x:Name="Normal"/>
<vsm:VisualState x:Name="MouseOver">
<Storyboard/>
</vsm:VisualState>
<vsm:VisualState x:Name="Pressed">
<Storyboard/>
</vsm:VisualState>
<vsm:VisualState x:Name="Disabled">
<Storyboard>
<DoubleAnimationUsingKeyFrames Storyboard.TargetName="DisabledVisualElement" Storyboard.TargetProperty="Opacity">
<SplineDoubleKeyFrame KeyTime="0" Value=".55"/>
</DoubleAnimationUsingKeyFrames>
</Storyboard>
</vsm:VisualState>
</vsm:VisualStateGroup>
<vsm:VisualStateGroup x:Name="FocusStates">
<vsm:VisualState x:Name="Focused">
<Storyboard>
<DoubleAnimationUsingKeyFrames Storyboard.TargetName="FocusVisualElement" Storyboard.TargetProperty="Opacity">
<SplineDoubleKeyFrame KeyTime="0" Value="1"/>
</DoubleAnimationUsingKeyFrames>
</Storyboard>
</vsm:VisualState>
<vsm:VisualState x:Name="Unfocused" />
</vsm:VisualStateGroup>
</vsm:VisualStateManager.VisualStateGroups>
<ContentPresenter
x:Name="contentPresenter"
Content="{TemplateBinding Content}"
ContentTemplate="{TemplateBinding ContentTemplate}"
VerticalAlignment="{TemplateBinding VerticalContentAlignment}"
HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}"
Margin="{TemplateBinding Padding}"/>
<Rectangle x:Name="DisabledVisualElement" RadiusX="3" RadiusY="3" Fill="#FFFFFFFF" Opacity="0" IsHitTestVisible="false" />
<Rectangle x:Name="FocusVisualElement" RadiusX="2" RadiusY="2" Margin="1" Stroke="#FF6DBDD1" StrokeThickness="1" Opacity="0" IsHitTestVisible="false" />
</Grid>
</ControlTemplate>
Now your button should be defined as:
<Button x:Name="NewAppointmentButton" Template="{StaticResource ButtonControlTemplate1}">
<TextBlock>X</TextBlock>
</Button>
If you're using expression blend you can use it to edit your button template to your heart's content :) Select your button in design view - just above the design window will be a grey button called 'NewAppointmentButton'. Click on it, then 'Edit control parts' then 'Edit template' - the button should get a yellow outline. You can now edit the visual elements and states and transitions.
Good luck!