This is also called "Master-Detail".
You can find a great tutorial here.
In short, you need to make the row selectable.
<asp:GridView ID="ProductsGrid" runat="server"
AutoGenerateColumns="False" DataKeyNames="ProductID"
DataSourceID="AllProductsDataSource" EnableViewState="False">
<Columns>
<asp:CommandField ShowSelectButton="True" />
<asp:BoundField DataField="ProductName"
HeaderText="Product" SortExpression="ProductName" />
<asp:BoundField DataField="UnitPrice"
DataFormatString="{0:c}" HeaderText="Unit Price"
HtmlEncode="False" SortExpression="UnitPrice" />
</Columns>
</asp:GridView>
This is done with <asp:CommandField ShowSelectButton="True" /> in the code above.
The next step is to add you DetailsView to be binded to the selected element of the master gridview. This can be done because the selection return the primary key of the element, from there you can load the detail.
This do a PostBack, if you want you can use Ajax and remove the PostBack flickering.