You can do something like this:
private void button1_Click(object sender, RoutedEventArgs e)
{
button2.Visibility = Visibility.Visible;
}
XAML:
<Button x:Name="button2" Content="Button" Visibility="Collapsed"/>
More here: http://msdn.microsoft.com/en-us/library/system.windows.visibility(v=vs.95).aspx