The Display date by default is the current date (DateTime.Now) and can be specified as an attribute on the date picker control in your xaml or within code.
If you are trying to get the date and format you will need to do something like the following:
<DatePicker HorizontalAlignment="Left" Margin="109,115,0,0" VerticalAlignment="Top" Name="DatePicker1"/>
string date1 = Convert.ToDateTime(DatePicker1.Text).ToString("yyyy-MM-dd");
Of course you could turn this into an extension method or add some safe guards so it won't blow up if you dont select a date at all. But that will allow you to format your selected date as you desire.