For detailed example refer,

ASP.Net GridView DetailsView Master Detail Example: Display selected GridView Row in DetailsView in ASP.Net

Please refer this code

HTML

<form id="form1" runat="server">
<div>
    <asp:GridView ID="GridView1" HeaderStyle-BackColor="#3AC0F2" HeaderStyle-ForeColor="White"
        runat="server" OnRowCommand="OnRowCommand" AutoGenerateColumns="false">
        <Columns>
            <asp:BoundField DataField="Id" HeaderText="Id" ItemStyle-Width="30" />
            <asp:BoundField DataField="Name" HeaderText="Name" ItemStyle-Width="150" />
            <asp:BoundField DataField="Country" HeaderText="Country" ItemStyle-Width="150" />
            <asp:TemplateField>
                <ItemTemplate>
                    <asp:LinkButton Text="Select" CommandName="Select" runat="server" />
                </ItemTemplate>
            </asp:TemplateField>
        </Columns>
    </asp:GridView>
    <hr />
    <asp:DetailsView ID="SelectedUser" runat="server" AutoGenerateRows="false">
        <Fields>
            <asp:TemplateField HeaderText="Id">
                <ItemTemplate>
                    <asp:TextBox ID="txtId" runat="server" Text='<%# Eval("Id") %>' />
                </ItemTemplate>
            </asp:TemplateField>
            <asp:TemplateField HeaderText="Name">
                <ItemTemplate>
                    <asp:TextBox ID="txtName" runat="server" Text='<%# Eval("Name") %>' />
                </ItemTemplate>
            </asp:TemplateField>
            <asp:TemplateField HeaderText="Country">
                <ItemTemplate>
                    <asp:TextBox ID="txtCountry" runat="server" Text='<%# Eval("Country") %>' />
                </ItemTemplate>
            </asp:TemplateField>
        </Fields>
    </asp:DetailsView>
</div>
</form>

Namespace

using System.Data;

C#

protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.AddRange(new DataColumn[3] { new DataColumn("Id", typeof(int)),
                    new DataColumn("Name", typeof(string)),
                    new DataColumn("Country",typeof(string)) });
        dt.Rows.Add(1, "John Hammond", "United States");
        dt.Rows.Add(2, "Mudassar Khan", "India");
        dt.Rows.Add(3, "Suzanne Mathews", "France");
        dt.Rows.Add(4, "Robert Schidner", "Russia");
        GridView1.DataSource = dt;
        GridView1.DataBind();
    }

}

protected void OnRowCommand(object sender, GridViewCommandEventArgs e)
{
    if (e.CommandName == "Select")
    {
        GridViewRow row = ((Control)e.CommandSource).NamingContainer as GridViewRow;
        DataTable dt = new DataTable();
        dt.Columns.AddRange(new DataColumn[3] { new DataColumn("Id", typeof(string)),
                    new DataColumn("Name", typeof(string)),
                    new DataColumn("Country",typeof(string)) });
        dt.Rows.Add(row.Cells[0].Text, row.Cells[1].Text, row.Cells[2].Text);
        SelectedUser.DataSource = dt;
        SelectedUser.DataBind();
    }
}

Screenshot