use following gridview selected index changed event
protected void GridView1_SelectedIndexChanged(object sender, EventArgs e)
{
string str = ((TextBox)GridView1.Rows[GridView1.SelectedIndex].FindControl("TextBox1")).Text;
}
put button command name as
select
<asp:TemplateField HeaderText="MyColumn">
<ItemTemplate>
<asp:Button ID="Button2" runat="server" Text="Save" CommandName="Select"/>
</ItemTemplate>
</asp:TemplateField>