You have a proerty called SelectedItem, this property represent your Row (is your selected object).
So in your TextBox, combobox or another control you can do Something like this, in your xaml.
Let me take the TextBox for the example:
<textbox text="{Binding ElementName=<b>nameofyourDataGrid</b>, Path=SelectedItem.<b>PropertyNameOfYourClass</b>}" />
Hope it helps. =)